- 在线时间
- 11 小时
- 最后登录
- 2012-1-13
- 注册时间
- 2011-12-22
- 听众数
- 4
- 收听数
- 0
- 能力
- 0 分
- 体力
- 418 点
- 威望
- 1 点
- 阅读权限
- 30
- 积分
- 204
- 相册
- 0
- 日志
- 0
- 记录
- 0
- 帖子
- 137
- 主题
- 43
- 精华
- 0
- 分享
- 0
- 好友
- 0
升级    52% TA的每日心情 | 开心
2012-1-13 11:05 |
|---|
签到天数: 15 天 [LV.4]偶尔看看III
|
对着S4群表看下面就能懂了，我曾把26字母乘群表带身上2月多, b& m* g/ u3 Z& e: G2 e! F5 z3 w
- [6 n. d9 q4 h! M8 X3 _& \S4 := Sym({ "a", "b", "c", "d" });
) O, h1 o* E7 j9 f> S4;
1 ?. F7 @8 [, o% g/ X8 yGenerators(S4);
8 |. P: G( f0 \1 x J9 N i9 EIsAbelian(S4);不是交换群7 K0 P2 E" k* \' Y1 H- B
Subgroups(S4: Al := "All") ;列出所有子群' o) H+ e" v5 n8 w, @0 N+ h
Subgroups(S4: Al := "Maximal") ;列出所有极大子群
, k ^, I; G D0 x8 q$ B9 o6 x* K! Y1 _8 k# j* p* f
SubgroupClasses(S4);
# o' `1 c. R1 ~4 T" a+ Z1 G! f m* ?: f4 M1 q
NormalSubgroups(S4);% ?3 W3 T3 q$ O, u
AbelianSubgroups(S4) ;
& t8 R* _0 x$ f! K( t/ ?MaximalSubgroups(S4) ;
( |! `0 r9 ?0 }: B# d9 G6 o2 q @% X, \# J- ]& x5 @# r9 w) t7 H
SubgroupLattice(S4);成格，你可画下这群包扩子群的图
1 G& P4 t& _3 B0 H. Q- o8 i
4 m k0 ^" c0 L- t! i$ EGSet(S4);
1 Z, M' S$ d9 L* E: @9 \1 AConjugacyClasses(S4);# S* i/ T4 |: J% n
NumberOfClasses(S4) ; 5类, }7 c+ k: r) i9 Y! F$ U
# `. L1 y4 ]: }6 Z
Symmetric group S4 acting on a set of cardinality 40 D$ c' m# ]% M6 O: Z
Order = 24 = 2^3 * 3& Z- e% U- K' m4 m+ L6 }8 F1 ]; D
{; J1 B! T% o- p" x- l9 ?
(c, b, a, d),! Y9 r: p, A i. r
(c, b)
% j* D7 i* Y$ C7 N7 k5 t) i7 O} 两生成元! J6 Q- y" {- x! ?4 v- d7 T, V" K
false' j+ \2 \0 c7 P" ^+ z5 E$ c" q
Conjugacy classes of subgroups 子群共扼类+ h2 ~9 e( f2 [1 L4 |
------------------------------/ }2 K- k0 v" l4 p6 O# L
( |; Y' U) G" ]) X$ ^$ S
[ 1] Order 1 Length 1
7 s3 z/ c, c7 [( N) h Permutation group acting on a set of cardinality 4
1 A' f: U2 u7 a Order = 1
& L0 A: u1 b" [8 f[ 2] Order 2 Length 3
) _5 w7 X1 k6 ~8 v Permutation group acting on a set of cardinality 4( O6 R5 O8 t& k3 n# J. s3 `! s: }! b
Order = 2
$ Z. M. H$ V2 N% h (c, d)(b, a)# T0 J) @! N W) E
[ 3] Order 2 Length 63 M3 z; h6 ?: |+ z
Permutation group acting on a set of cardinality 4
/ _) W; V+ d) P7 Z; r Order = 2
0 H; J( K( u% k3 c* O (a, d)1 q# S* n! c, _' L/ T0 v H: x
[ 4] Order 3 Length 4
1 \( G8 N) e; J5 p Permutation group acting on a set of cardinality 4
# p6 j9 k2 R0 `) u: D E" w4 s O, Y Order = 3
4 y6 a1 f3 I4 \1 J/ [2 o- K (b, a, d)3 @$ b" t" m0 `, `9 i
[ 5] Order 4 Length 1$ b* M, n {& y) }6 z7 A. e
Permutation group acting on a set of cardinality 4
6 Y3 V# S0 f8 d6 ~% W8 P Order = 4 = 2^2
% `$ t! P( k! M- ?5 m9 Y, t (c, d)(b, a)
3 X' H) v8 e+ g (c, a)(b, d)% w5 Z5 s4 _& k3 b! |: ?
[ 6] Order 4 Length 3
0 c9 v# u( Y0 C Permutation group acting on a set of cardinality 4
4 {3 t# Z# @$ k7 p7 j Order = 4 = 2^2. K& F5 n) ^$ T0 y @
(c, d, b, a): g4 D/ e# B, v9 G1 A
(c, b)(a, d)
" Q0 ?% U( s% a, J[ 7] Order 4 Length 3
4 L( N1 i; c: A" O Permutation group acting on a set of cardinality 4/ y1 ?, K' J' r
Order = 4 = 2^2
3 H' H4 X0 @2 A6 l. }8 X (a, d)3 d& H( Z7 c0 ^! H
(c, b)(a, d)
+ Y& ?, S- [7 D5 W[ 8] Order 6 Length 45 d; j3 {9 s; V+ s
Permutation group acting on a set of cardinality 4! t* {. O4 R+ Q z. h
Order = 6 = 2 * 3
7 Z( x9 c6 z m* h (a, d)
" ?$ p% ^6 _+ r (b, a, d)
( V# b( b8 q. x2 P& x5 I[ 9] Order 8 Length 3
$ Q* g a! z, d4 o L. C4 O% n3 p Permutation group acting on a set of cardinality 40 G9 z/ f- o9 [0 Z
Order = 8 = 2^36 Q9 w0 E( w) j& F, R
(a, d)* e0 s' ?$ z: s# g; k n$ c
(c, d)(b, a)
9 c/ W6 L) C- Q6 O i0 [+ e9 L (c, a)(b, d)1 a1 j* U7 A1 H4 F7 ^) l3 _& t+ i
[10] Order 12 Length 10 H: h( z* D7 a& u" M$ X( @# F
Permutation group acting on a set of cardinality 4; e, ^& F7 }" m' c& u- z3 q& G* e
Order = 12 = 2^2 * 3
0 s/ U2 y3 g. Z) S/ l (b, a, d)
% W- r1 F) v- k) ^ (c, d)(b, a) m6 A" v" ` {
(c, a)(b, d)
, | r9 Z) a8 q7 @4 ][11] Order 24 Length 1
2 Z/ U) u7 H; a7 }5 ^ Permutation group acting on a set of cardinality 4
1 k. U/ J% W& d ~ Order = 24 = 2^3 * 3
8 R6 |$ o5 }9 O2 W (a, d)
! A, V/ X6 M6 i6 Y (b, a, d)
! [% Y& t3 G- u ~% a" t (c, d)(b, a)
' Q7 X! T" l# X/ e (c, a)(b, d)
; z8 O" e: M% ~( `' ?Conjugacy classes of subgroups$ b4 Y1 ~& Z0 o+ ^
------------------------------9 p' U F$ P' l7 h& T0 p. l
. N0 e* p8 {! S, D3 e[1] Order 6 Length 4) A, D, G" A3 z O* k7 J
Permutation group acting on a set of cardinality 4
' P) H" ~9 S1 u$ L Order = 6 = 2 * 3
( \6 f6 r* q) O (a, d)
) K* _3 {# S: ]( F' o+ c (b, a, d)
7 z7 W$ F" E2 [6 x1 \' W! z* p[2] Order 8 Length 33 v5 M0 {6 W* C! z
Permutation group acting on a set of cardinality 48 u1 h# N+ i8 Z# F; a
Order = 8 = 2^3: D9 f% L/ \1 Y0 R+ ?2 l
(a, d): u) M& N3 v# Y8 D: n
(c, d)(b, a)
9 g- f) ?5 f4 Z# F# w# \ (c, a)(b, d)
; [ l3 S# M! g2 o! }4 W[3] Order 12 Length 1' e2 w( q/ d5 H9 C X& v
Permutation group acting on a set of cardinality 4
5 m3 E+ e0 f, _% u& `3 S c Order = 12 = 2^2 * 3
* y1 e2 Z. }# t I) c n4 Z- A (b, a, d)5 C& k! Q* E. _. j
(c, d)(b, a)
: {5 V# \# g7 N (c, a)(b, d)
( \& c1 J4 F2 c0 o7 ZConjugacy classes of subgroups/ Y: Z# P, B/ a' `
------------------------------( S% [+ v* L+ A" v
" f$ |( f' ~: H$ q: N
[ 1] Order 1 Length 1
h$ w9 G7 r( B( h. B w Permutation group acting on a set of cardinality 4
. c8 Y& }4 M) p( P6 f% e3 S Order = 1
3 g- ~5 B0 [* m[ 2] Order 2 Length 3
4 k5 s7 |" R0 ^8 K3 R# O# J) k Permutation group acting on a set of cardinality 4
1 K; i% m p5 A: ^- ^( ? Order = 20 g8 {* l% W8 I1 A
(c, d)(b, a)
+ Q, A% b. |3 `- G' P[ 3] Order 2 Length 6
6 W! o1 I1 N3 @( Y; I/ {4 X' M Permutation group acting on a set of cardinality 4
9 L) q. J8 {5 S4 @ Order = 2
1 Q" a& j; w$ s7 N (a, d)
$ J: I$ ~5 r: V: G" w[ 4] Order 3 Length 4* R L$ ]: Z$ K! ]8 M) m. n2 S2 u+ k
Permutation group acting on a set of cardinality 4
6 Q% ?3 \* n! |1 ]. N Order = 3. y$ G1 y4 c9 G( A+ F0 u
(b, a, d)
9 W# T/ e5 `! h- `! ` Y[ 5] Order 4 Length 13 J: ~$ |7 i4 c- q9 n' P
Permutation group acting on a set of cardinality 4* d8 h; H C2 I) \$ e/ T. u3 S
Order = 4 = 2^27 D4 K* y7 b1 R5 S: P& w
(c, d)(b, a)
# R# ?+ ]1 p2 }$ o& b# s1 X( h (c, a)(b, d)
; G. r; C. `. h- @& p[ 6] Order 4 Length 3$ ^4 l6 ^6 v- k/ T5 E
Permutation group acting on a set of cardinality 4
. O2 M0 H. C6 ^ Order = 4 = 2^2- d2 x7 n: o( u( R4 e6 y
(c, d, b, a)
' b0 u" F# |4 K1 n- A! E (c, b)(a, d)
1 E5 H m3 I0 v! x[ 7] Order 4 Length 3/ l8 A& q4 t$ Y% x2 r5 m; A
Permutation group acting on a set of cardinality 4/ ]5 i7 J8 m* {& k: |0 t
Order = 4 = 2^2
: @6 q4 M9 H0 s6 H7 O, p+ c/ T (a, d)1 S3 j0 y, M7 N; Z
(c, b)(a, d)4 z! O6 G1 J( k1 _& X
[ 8] Order 6 Length 4( i3 i7 ^2 z9 q2 Z$ }
Permutation group acting on a set of cardinality 43 {; H; n* q$ U( X/ I5 F; n
Order = 6 = 2 * 3
. P, ~+ T3 k/ M4 I% Z" R) ], S (a, d)
- }6 g0 R! K- I6 q6 L J (b, a, d)2 m+ E( M" c- F- v3 N
[ 9] Order 8 Length 3% C. R, A. s4 d; Y& G" @5 j5 {
Permutation group acting on a set of cardinality 4* q6 L3 b8 p( l$ w8 _& ~: D
Order = 8 = 2^3
2 d, K, R& R1 a6 z (a, d), h: R2 [% u5 a7 h' W. Q# `- L
(c, d)(b, a)
Q4 H8 {/ K+ R (c, a)(b, d)5 h2 T$ H4 z8 g
[10] Order 12 Length 1
% u, \$ {& J; [& O2 m& U& n/ ]( {* l Permutation group acting on a set of cardinality 4
) Z; s9 w) q( p2 x: V Order = 12 = 2^2 * 3
1 S$ y, e. \0 g- E. G (b, a, d)
0 B1 L1 U- R% X: y" H7 W" _3 t (c, d)(b, a)
8 V1 e! Q' d% f$ ?6 E! M5 _ (c, a)(b, d)6 L. B7 o3 w& r& r) Z+ C
[11] Order 24 Length 1
! f, E* X- E" S- d8 E' B" F Permutation group acting on a set of cardinality 46 q' i+ L, p" f/ s% [
Order = 24 = 2^3 * 3
3 g% b" l" K1 D- w$ N (a, d)
+ Y( l# _: w: N% I* @ p (b, a, d)4 w8 L0 J" t& O* [" p, U
(c, d)(b, a)& f' j+ G4 _2 ]7 x8 }% ^& G/ }
(c, a)(b, d)
! s8 w& t- w; t$ o8 ]% p- j: ^Conjugacy classes of subgroups4 m/ K# C# H6 c0 w7 T* J
------------------------------( X7 ^7 z: D: a1 l, m) J
( \4 O% f- i6 U G[1] Order 1 Length 1
3 x8 Y) }) L4 X, l Permutation group acting on a set of cardinality 4" J2 ]. I4 ?- F" o
Order = 1
; {, {' O$ n' @& D+ D[2] Order 4 Length 1
; ?% {* W M' u! ]# p: v) h Permutation group acting on a set of cardinality 4
& m3 O0 a9 e; @% \ Order = 4 = 2^2
+ t- Q7 a% {5 n, b7 A (c, d)(b, a)
: a N: g" @3 }: q5 H7 ]4 Y (c, a)(b, d): t$ b5 q/ x: v7 `
[3] Order 12 Length 1
" v9 P B/ S( L w" n, R: W Permutation group acting on a set of cardinality 4* A4 r& Y& k/ _. \
Order = 12 = 2^2 * 3+ S# b ~$ Y* n7 {
(b, a, d)
& h2 {; T7 z2 e* M (c, d)(b, a)7 c; ~1 U9 V8 q& Q, g3 i
(c, a)(b, d)
5 Z6 y4 @% r7 N) |2 k[4] Order 24 Length 1
0 }; Y. d- _4 J9 H$ g Permutation group acting on a set of cardinality 4
9 R% `- u1 p! R Order = 24 = 2^3 * 33 x3 ^+ p# j3 h
(a, d)' t; r% Q3 p, q0 {4 X$ g
(b, a, d)
$ O. {" a. q8 {( B (c, d)(b, a)
0 m+ E* |# y j/ X& W2 M4 w (c, a)(b, d)* }, v7 W; [& @5 m9 x
Conjugacy classes of subgroups! z( e' W9 N' b! Y3 [- [
------------------------------
; e2 N1 A2 O! p" l" q( p( b, d# ~4 i
[1] Order 1 Length 11 J6 S( M/ [: O
Permutation group acting on a set of cardinality 4
# ^" Z" h* p$ o) u9 `3 K) @ Order = 1( U i: T2 h M6 v! `) A
[2] Order 2 Length 3
; {! o3 P; f5 s' N. r7 c. v7 Y Permutation group acting on a set of cardinality 4
' j7 [9 U0 c; r) X v0 P, Q Order = 2
7 v$ T! M$ b5 Q, b (c, d)(b, a)
4 G8 S8 C- Z& o4 E+ w+ [6 p& j[3] Order 2 Length 6
- d3 w: W* H" u- ]: | Permutation group acting on a set of cardinality 4! A2 K' G: z9 B! p* B( T
Order = 26 F: ^. w1 \) c( d, U! {+ Y
(a, d)
7 w. I) y- l( _[4] Order 3 Length 4
# w' s3 Z+ [& M+ Q0 `. V Permutation group acting on a set of cardinality 4
1 M* M* C0 U0 ]& M% I Order = 3
! r0 S5 X4 n+ b ]. m. M (b, a, d)" @4 `4 d) ?7 X' |/ B& t0 v! ~/ g
[5] Order 4 Length 1* q2 f1 F9 L* e) w9 _# W5 G/ _
Permutation group acting on a set of cardinality 4$ x& g+ d+ h8 Q/ b
Order = 4 = 2^26 f, p! o& Y& Q/ m$ M
(c, d)(b, a)
6 X) z$ _' C9 J; X (c, a)(b, d)
! ]% l+ B- c; R9 }1 T" }[6] Order 4 Length 3
' }2 k4 z$ ?( r1 V8 Y) f Permutation group acting on a set of cardinality 4
' P8 Q+ Z2 @) ~2 _" C1 \7 g2 q Order = 4 = 2^24 R* K' | A0 S1 E5 Z- q$ L
(c, d, b, a)
" h8 m$ f+ M4 l4 m( c4 |! ? (c, b)(a, d)
. T4 l0 G1 Z' O+ a7 o7 s# I& |# B[7] Order 4 Length 38 j! y, y4 z/ Y; g- y# p2 M. Z
Permutation group acting on a set of cardinality 4! g! T4 r3 ?: D. m% G/ w$ |; U
Order = 4 = 2^2
7 X8 {0 b; K$ R% j* z (a, d)
1 X& n& w$ b6 k% Z (c, b)(a, d)
8 Z, G9 c! n, AConjugacy classes of subgroups; ~* k9 `9 r, V2 w+ E
------------------------------1 @4 y' a }8 P9 ^; d3 Z# b
, m" j" E1 z" E( H+ I[1] Order 6 Length 4
( b1 e% m$ v7 } t: \1 N Permutation group acting on a set of cardinality 45 n7 ]7 T$ r' u* s: O3 [6 @
Order = 6 = 2 * 3( A, `2 h( d5 I5 n4 t6 G9 S9 a
(a, d)
) a4 B; i- Q8 G5 n5 g) _ (b, a, d)
& P; d3 M; D& W- i! E+ w' L* b[2] Order 8 Length 3' _5 L& ~' Q$ g: ~: h S: b
Permutation group acting on a set of cardinality 4& k1 k6 d }7 ]9 Q; P# D: W. U) `
Order = 8 = 2^3
- ~) N9 s2 b% P4 S0 @3 U' S4 o (a, d)
# G' p& q3 _7 ], F3 g. K* T (c, d)(b, a)( Q, ?! [: P' a+ y7 _' ^& B. [0 T
(c, a)(b, d)
U' c8 I3 ?# q5 ?& f8 g[3] Order 12 Length 1* f- j: y4 }) D7 k
Permutation group acting on a set of cardinality 45 w1 q; N6 D2 O# w+ V: j) V( x8 ^
Order = 12 = 2^2 * 36 Z! _7 z: t! s5 h& I$ Z0 E
(b, a, d)) K9 H5 C: J- E/ G7 B( w* W
(c, d)(b, a)
/ N* T7 D( a0 {) B8 Z (c, a)(b, d)
; W, }9 V. D0 V; U& `% d* ]% y& X$ C" p! }2 p3 M
Partially ordered set of subgroup classes \# e1 T1 j* x0 ^
-----------------------------------------; N. u& d9 ]; {# k* x
7 S7 p4 @" q4 Z( v$ t! L[11] Order 24 Length 1 Maximal Subgroups: 8 9 10
# M* p) h. B# w! O& g! r8 e2 E2 r---
0 N; V2 y, O' }8 |0 V! r[10] Order 12 Length 1 Maximal Subgroups: 4 5$ O; `- _& \9 o! b" v# }
[ 9] Order 8 Length 3 Maximal Subgroups: 5 6 7
; Z3 n: X, F3 _5 K. D---9 ?& c# ^$ {; h/ [
[ 8] Order 6 Length 4 Maximal Subgroups: 3 43 i" K) U/ D/ J5 N# Z9 @
[ 7] Order 4 Length 3 Maximal Subgroups: 29 S$ J8 s2 W, }6 P3 j: B
[ 6] Order 4 Length 3 Maximal Subgroups: 2 3
. R5 z& d ?# Z5 M7 {& v, t2 a[ 5] Order 4 Length 1 Maximal Subgroups: 2
, d5 U* D' M" ?; K---
/ ~6 C- I7 `( Q! Q5 s! g: g0 Q9 P[ 4] Order 3 Length 4 Maximal Subgroups: 1
+ g2 m% y) m# {6 \[ 3] Order 2 Length 6 Maximal Subgroups: 1
2 t# z7 P- s* N5 c; E8 [[ 2] Order 2 Length 3 Maximal Subgroups: 1
) m; @& u3 S3 w1 n; {1 T% C---. ]( i1 r( R& Y( d4 Q. L- b
[ 1] Order 1 Length 1 Maximal Subgroups:
5 c/ C( S! H* `6 ?) y! \3 `
3 V" T) N& v, u0 T- e, hGSet{@ c, b, a, d @}: o. j% S8 ^2 i$ w) B
Conjugacy Classes of group S42 `, v: x$ `# w8 W/ m: Y
-----------------------------
$ L9 E9 q) x1 e: A[1] Order 1 Length 1
* W5 ]8 Y! Q) a ^ Rep Id(S4)
% u) W2 @+ B2 z G# ~) R6 A, V* a% b' D7 }: | s, h
[2] Order 2 Length 3
1 N$ r7 J6 p) P/ X: d$ p. L Rep (c, b)(a, d)
% Q' |: W, p+ w h! z% a! d8 K6 W5 ~& H- x
[3] Order 2 Length 6
- W; j$ i# L/ F: q Rep (c, b)
* v; P( c1 ^: y# i h u- R* _& X% k; i+ i% _" S0 b
[4] Order 3 Length 8
7 [6 S3 T' d: N8 x+ V9 s9 X Rep (c, b, a)
+ M; U7 n6 |' X- [ e' h0 P. B! t/ L! a3 w2 O- B/ ]
[5] Order 4 Length 6 0 R. W- f2 B4 V2 W$ D7 I, B
Rep (c, b, a, d)( Q* [" D) k* K6 s$ a
$ b! w6 f9 k3 u
* h+ A4 X5 m2 y/ M0 _7 `* f9 E
5 |
|
IP卡
狗仔卡
发表于 2011-12-29 00:36
转播
淘帖
分享
收藏
支持
反对
微信
提升卡
置顶卡
沉默卡
喧嚣卡
变色卡
抢沙发
显身卡
