Question

Counting number of p-Sylow subgroups in $A_n$

score 372 · Answer 1 · 2026-04-16 04:55:28

372

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Counting number of p-Sylow subgroups in $A_n$

Published on 16 Apr 2026 - 4:55

score 264 · Answer 2 · 2026-04-16 13:27:08

264

Views

Key-space for a restricted substitution cipher

Published on 16 Apr 2026 - 13:27

score 358 · Answer 3 · 2026-04-13 20:55:47

358

Views

If $\mathrm{Stab}(x)_{S_5} \nsubseteq A_5$ then how to prove $[\mathrm{Stab}(x)_{S_5} : \mathrm{Stab}(x)_{A_5}]=2$? Please help

Published on 13 Apr 2026 - 20:55

score 793 · Answer 4 · 2026-04-14 12:43:00

793

Views

Showing that the alternating group of degree n is normal

Published on 14 Apr 2026 - 12:43

score 2.2k · Answer 5 · 2026-04-10 18:49:54

2.2k

Views

How many permutations of $[n]$ are cycles of length $n$?

Published on 10 Apr 2026 - 18:49

score 437 · Answer 6 · 2026-04-13 18:34:13

437

Views

Computing the product of disjoint cycles

Published on 13 Apr 2026 - 18:34

score 195 · Answer 7 · 2026-04-16 09:56:34

195

Views

If P is an nxn permutation matrix, is there an upper bound on k such that $P^k = I$?

Published on 16 Apr 2026 - 9:56

score 174 · Answer 8 · 2026-05-10 14:31:56

174

Views

Products of permutation cycles

Published on 10 May 2026 - 14:31

score 206 · Answer 9 · 2026-04-14 16:38:33

206

Views

Question on generating sets of $S_n$

Published on 14 Apr 2026 - 16:38

score 99 · Answer 10 · 2026-04-13 18:13:05

99

Views

Prove $(\rho_1 \rho_2 \cdots \rho_r)^u = e \implies e=\rho_1^u=\rho_2^u=\cdots=\rho_r^u$

Published on 13 Apr 2026 - 18:13

score 217 · Answer 11 · 2026-04-17 11:40:38

217

Views

Abstract Algebra Proof with cycles and transpositions

Published on 17 Apr 2026 - 11:40

score 81 · Answer 12 · 2026-04-16 03:58:56

81

Views

Why did this reversal from the left cosets of $\langle (1, 2, 3) \rangle$ in $A_4$ give me the right cosets?

Published on 16 Apr 2026 - 3:58

score 73 · Answer 13 · 2026-04-12 22:46:18

73

Views

Relationship between order of $(x,y)$ in $G \times G'$ and order of disjoint permutations, which both involve LCMs?

Published on 12 Apr 2026 - 22:46

score 929 · Answer 14 · 2026-04-16 04:10:52

929

Views

Elements of $S_n$ can be written as a product of $k$-cycles.

Published on 16 Apr 2026 - 4:10

score 711 · Answer 15 · 2026-04-16 10:12:31

711

Views

Let $\sigma\in S_n$ be an $n$-cycle, and let $\tau\in S_n$ be a $2$-cycle. Then, $\sigma$ and $\tau$ need not generate $S_n$.

Published on 16 Apr 2026 - 10:12

List Question

Counting number of p-Sylow subgroups in $A_n$

Key-space for a restricted substitution cipher

If $\mathrm{Stab}(x)_{S_5} \nsubseteq A_5$ then how to prove $[\mathrm{Stab}(x)_{S_5} : \mathrm{Stab}(x)_{A_5}]=2$? Please help

Showing that the alternating group of degree n is normal

How many permutations of $[n]$ are cycles of length $n$?

Computing the product of disjoint cycles

If P is an nxn permutation matrix, is there an upper bound on k such that $P^k = I$?

Products of permutation cycles

Question on generating sets of $S_n$

Prove $(\rho_1 \rho_2 \cdots \rho_r)^u = e \implies e=\rho_1^u=\rho_2^u=\cdots=\rho_r^u$

Abstract Algebra Proof with cycles and transpositions

Why did this reversal from the left cosets of $\langle (1, 2, 3) \rangle$ in $A_4$ give me the right cosets?

Relationship between order of $(x,y)$ in $G \times G'$ and order of disjoint permutations, which both involve LCMs?

Elements of $S_n$ can be written as a product of $k$-cycles.

Let $\sigma\in S_n$ be an $n$-cycle, and let $\tau\in S_n$ be a $2$-cycle. Then, $\sigma$ and $\tau$ need not generate $S_n$.

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