Question

If G acts on X, show that there must be a fixed point for this action. Please help.

score 6.2k · Answer 1 · 2026-03-27 18:26:53

6.2k

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If G acts on X, show that there must be a fixed point for this action. Please help.

Published on 27 Mar 2026 - 18:26

score 7.4k · Answer 2 · 2026-03-31 18:49:00

7.4k

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Online Finite Field Calculator

Published on 31 Mar 2026 - 18:49

score 518 · Answer 3 · 2014-04-21 13:43:22

518

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Show that $Z_{p^2} \oplus Z_{p^2}$ has exactly one subgroup isomorphic to $Z_p \oplus Z_p$

Published on 21 Apr 2014 - 13:43

score 66 · Answer 4 · 2026-03-28 10:35:05

66

Views

Abstract Algebra: prove it is cyclic

Published on 28 Mar 2026 - 10:35

score 554 · Answer 5 · 2026-03-25 03:23:02

554

Views

Expressing a matrix in terms of subgroup generators using Magma

Published on 25 Mar 2026 - 3:23

score 109 · Answer 6 · 2014-04-21 20:10:24

109

Views

What is the index of $\mathrm{diag}(G)$ in $G \times G$ if $G$ is a finite group?

Published on 21 Apr 2014 - 20:10

score 722 · Answer 7 · 2026-03-26 21:26:07

722

Views

Show that if the prime $p$ divides $|G|$, then $|X|$ is divisible by $p$.

Published on 26 Mar 2026 - 21:26

score 646 · Answer 8 · 2026-03-26 08:00:53

646

Views

$ |G_1 |$ and $|G_2 | $ are coprime. Show that $K = H_1 \times H_2$

Published on 26 Mar 2026 - 8:00

score 113 · Answer 9 · 2014-04-22 21:47:32

113

Views

Dihedralize Twice - dihedralize a dihedral group $D_n$

Published on 22 Apr 2014 - 21:47

score 4k · Answer 10 · 2014-04-23 00:49:54

4k

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Groups with $|G| = p^2q$. Prove that if $p$ and $q$ are primes, then there are no simple groups of order $p^2q$.

Published on 23 Apr 2014 - 0:49

score 78 · Answer 11 · 2026-03-26 14:40:44

78

Views

Ruling out orders when applying Sylow's theorems

Published on 26 Mar 2026 - 14:40

score 71 · Answer 12 · 2014-04-23 04:07:18

71

Views

Suppose that $|G| = p^aq$, where p and q are primes and a > 0, Then $G$ is not simple?

Published on 23 Apr 2014 - 4:07

score 478 · Answer 13 · 2026-03-25 08:12:49

478

Views

Size of maximal tori in finite simple groups of Lie type

Published on 25 Mar 2026 - 8:12

score 589 · Answer 14 · 2026-03-27 23:00:46

589

Views

Classifying $\mathbb{Z}_{12} \times \mathbb{Z}_3 \times \mathbb{Z}_6/\langle(8,2,4)\rangle$

Published on 27 Mar 2026 - 23:00

score 3.6k · Answer 15 · 2026-03-27 22:53:56

3.6k

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Let $G$ be a finite abelian group and let $p$ be a prime that divides order of $G$. then $G$ has an element of order $p$

Published on 27 Mar 2026 - 22:53

List Question

If G acts on X, show that there must be a fixed point for this action. Please help.

Online Finite Field Calculator

Show that $Z_{p^2} \oplus Z_{p^2}$ has exactly one subgroup isomorphic to $Z_p \oplus Z_p$

Abstract Algebra: prove it is cyclic

Expressing a matrix in terms of subgroup generators using Magma

What is the index of $\mathrm{diag}(G)$ in $G \times G$ if $G$ is a finite group?

Show that if the prime $p$ divides $|G|$, then $|X|$ is divisible by $p$.

$ |G_1 |$ and $|G_2 | $ are coprime. Show that $K = H_1 \times H_2$

Dihedralize Twice - dihedralize a dihedral group $D_n$

Groups with $|G| = p^2q$. Prove that if $p$ and $q$ are primes, then there are no simple groups of order $p^2q$.

Ruling out orders when applying Sylow's theorems

Suppose that $|G| = p^aq$, where p and q are primes and a > 0, Then $G$ is not simple?

Size of maximal tori in finite simple groups of Lie type

Classifying $\mathbb{Z}_{12} \times \mathbb{Z}_3 \times \mathbb{Z}_6/\langle(8,2,4)\rangle$

Let $G$ be a finite abelian group and let $p$ be a prime that divides order of $G$. then $G$ has an element of order $p$

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