Question

If a group has a normal subgroup of order $d$ for every divisor $d$ of the order of the group then it is nilpotent

score 435 · Answer 1 · 2026-03-25 12:49:46

435

Views

If a group has a normal subgroup of order $d$ for every divisor $d$ of the order of the group then it is nilpotent

Published on 25 Mar 2026 - 12:49

score 532 · Answer 2 · 2026-04-10 12:36:37

532

Views

Finding $n$ elements of $\mathbb{Z}_n\times\mathbb{Z}_n$ such that their differences are all different

Published on 10 Apr 2026 - 12:36

score 419 · Answer 3 · 2026-03-27 19:53:41

419

Views

Showing Sylow $p$-subgroup is an elementary abelian $p$-group

Published on 27 Mar 2026 - 19:53

score 214 · Answer 4 · 2026-03-27 19:53:33

214

Views

In proving Sylow's Theorem (1), how could we start by assuming inductively that Sylow p-subgroups exist?

Published on 27 Mar 2026 - 19:53

score 62 · Answer 5 · 2026-04-11 18:32:13

62

Views

normalizer tower question

Published on 11 Apr 2026 - 18:32

score 213 · Answer 6 · 2026-04-10 19:26:36

213

Views

Reflection groups of division rings

Published on 10 Apr 2026 - 19:26

score 139 · Answer 7 · 2019-12-31 00:05:44

139

Views

Finding two group elements $x,y$ in a finite group such that $|xy|$ is greater than $|x| |y|$

Published on 31 Dec 2019 - 0:05

score 31 · Answer 8 · 2026-03-26 01:12:37

31

Views

If every conjugacy class of $C$ is even, then every finite-dimensional representation $V$ of $G$ over $F$ satisfies $V\simeq V^*$

Published on 26 Mar 2026 - 1:12

score 39 · Answer 9 · 2026-04-10 17:06:48

39

Views

Generalizing CIT-groups to odd case

Published on 10 Apr 2026 - 17:06

score 985 · Answer 10 · 2020-01-01 20:15:34

985

Views

Number of ways to label die with opposing faces summing to 7

Published on 01 Jan 2020 - 20:15

score 224 · Answer 11 · 2026-04-08 08:17:38

224

Views

natural map $SL_2(\mathbb{Z})\to SL_2(\mathbb{Z}/n\mathbb{Z})$ is surjective

Published on 08 Apr 2026 - 8:17

score 41 · Answer 12 · 2020-01-02 19:16:12

41

Views

Is any finite indecomposable group of exponent $4$ isomorphic either to $C_4$ or to $Q_8$?

Published on 02 Jan 2020 - 19:16

score 193 · Answer 13 · 2026-03-26 01:08:03

193

Views

No simple group of order $2^73^2$

Published on 26 Mar 2026 - 1:08

score 1.1k · Answer 14 · 2026-04-11 07:45:56

1.1k

Views

Clean and clever proofs to show every homomorphism of two groups with coprime orders is trivial?

Published on 11 Apr 2026 - 7:45

score 214 · Answer 15 · 2026-03-25 19:16:15

214

Views

Finite groups with elements of order a prime power

Published on 25 Mar 2026 - 19:16

List Question

If a group has a normal subgroup of order $d$ for every divisor $d$ of the order of the group then it is nilpotent

Finding $n$ elements of $\mathbb{Z}_n\times\mathbb{Z}_n$ such that their differences are all different

Showing Sylow $p$-subgroup is an elementary abelian $p$-group

In proving Sylow's Theorem (1), how could we start by assuming inductively that Sylow p-subgroups exist?

normalizer tower question

Reflection groups of division rings

Finding two group elements $x,y$ in a finite group such that $|xy|$ is greater than $|x| |y|$

If every conjugacy class of $C$ is even, then every finite-dimensional representation $V$ of $G$ over $F$ satisfies $V\simeq V^*$

Generalizing CIT-groups to odd case

Number of ways to label die with opposing faces summing to 7

natural map $SL_2(\mathbb{Z})\to SL_2(\mathbb{Z}/n\mathbb{Z})$ is surjective

Is any finite indecomposable group of exponent $4$ isomorphic either to $C_4$ or to $Q_8$?

No simple group of order $2^73^2$

Clean and clever proofs to show every homomorphism of two groups with coprime orders is trivial?

Finite groups with elements of order a prime power

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