Question

If $|G| = p^nq$ then $G$ has only one normal subgroup of order $q$

score 340 · Answer 1 · 2026-05-05 14:35:38

340

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If $|G| = p^nq$ then $G$ has only one normal subgroup of order $q$

Published on 05 May 2026 - 14:35

score 65 · Answer 2 · 2026-05-03 17:47:54

65

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How to show that every group in the normal series of $G$ is normal in $G$

Published on 03 May 2026 - 17:47

score 116 · Answer 3 · 2026-05-10 11:21:50

116

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Two abelian groups $|G| =n $ and $|H|=n$ are isomorphic if and only if they have same number of elements of order $m$,$1\le m\le n$

Published on 10 May 2026 - 11:21

score 204 · Answer 4 · 2026-05-04 08:58:28

204

Views

Finite groups with 15 or 16 conjugacy classes

Published on 04 May 2026 - 8:58

score 60 · Answer 5 · 2026-04-11 00:05:59

60

Views

Proof Group Homomorphism: $\varphi(e)= e'$ & $\varphi(\hat{a})= \widehat{\varphi(a)}$

Published on 11 Apr 2026 - 0:05

score 177 · Answer 6 · 2026-05-10 13:26:22

177

Views

How order of an element and gcd related for abelian groups

Published on 10 May 2026 - 13:26

score 289 · Answer 7 · 2026-05-10 13:51:32

289

Views

Is there a neat way to see that $C_3$ is not a quotient of $S_n$?

Published on 10 May 2026 - 13:51

score 178 · Answer 8 · 2026-05-10 16:34:58

178

Views

Role of Well-Ordering Principle in proving every subgroup of $\mathbb{Z}$ is of the form $n\mathbb{Z}$

Published on 10 May 2026 - 16:34

score 72 · Answer 9 · 2026-04-29 12:53:12

72

Views

Show that no group has $D_n$ as its derived subgroup.

Published on 29 Apr 2026 - 12:53

score 290 · Answer 10 · 2026-05-05 10:19:33

290

Views

$\mathrm{Hom}(\mathrm{Hom}(G,H),H) \simeq G$?

Published on 05 May 2026 - 10:19

score 89 · Answer 11 · 2026-05-10 12:35:46

89

Views

Finding the Galois group of $\mathbb{Q}(\alpha,i)|\mathbb{Q}$, whereby $\alpha^2 = \frac{3}{2}+\frac{1}{2}i\sqrt7$

Published on 10 May 2026 - 12:35

score 54 · Answer 12 · 2026-04-14 04:20:26

Does the set of $n\times n$ invertible matrices with real coeffs where the sum of each row and column sums to one forms a group under multiplication?

score 121 · Answer 13 · 2026-04-17 13:11:14

121

Views

What is the smallest group containing $f$ and $g$ isomorphic to?

Published on 17 Apr 2026 - 13:11

score 106 · Answer 14 · 2026-03-31 23:28:19

106

Views

A general definition of compatibility of geometrical structures

Published on 31 Mar 2026 - 23:28

score 49 · Answer 15 · 2026-05-10 13:50:46

49

Views

$Z(G)O_p(G) = Z_{p'}(G)O_p(G)$?

Published on 10 May 2026 - 13:50

List Question

If $|G| = p^nq$ then $G$ has only one normal subgroup of order $q$

How to show that every group in the normal series of $G$ is normal in $G$

Two abelian groups $|G| =n $ and $|H|=n$ are isomorphic if and only if they have same number of elements of order $m$,$1\le m\le n$

Finite groups with 15 or 16 conjugacy classes

Proof Group Homomorphism: $\varphi(e)= e'$ & $\varphi(\hat{a})= \widehat{\varphi(a)}$

How order of an element and gcd related for abelian groups

Is there a neat way to see that $C_3$ is not a quotient of $S_n$?

Role of Well-Ordering Principle in proving every subgroup of $\mathbb{Z}$ is of the form $n\mathbb{Z}$

Show that no group has $D_n$ as its derived subgroup.

$\mathrm{Hom}(\mathrm{Hom}(G,H),H) \simeq G$?

Finding the Galois group of $\mathbb{Q}(\alpha,i)|\mathbb{Q}$, whereby $\alpha^2 = \frac{3}{2}+\frac{1}{2}i\sqrt7$

Does the set of $n\times n$ invertible matrices with real coeffs where the sum of each row and column sums to one forms a group under multiplication?

What is the smallest group containing $f$ and $g$ isomorphic to?

A general definition of compatibility of geometrical structures

$Z(G)O_p(G) = Z_{p'}(G)O_p(G)$?

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