Question

If G is a group, $H< G^{|G|}$ and $|H|\geq 2^{|G|}$, then can $H$ be cyclic?

score 66 · Answer 1 · 2022-04-02 03:43:56

66

Views

If G is a group, $H< G^{|G|}$ and $|H|\geq 2^{|G|}$, then can $H$ be cyclic?

Published on 02 Apr 2022 - 3:43

score 1k · Answer 2 · 2022-04-05 18:20:16

1k

Views

Proof that if $G$ is a group with no proper subgroups and order $>1$, then $G$ is cyclic with prime order

Published on 05 Apr 2022 - 18:20

score 308 · Answer 3 · 2022-04-11 16:36:26

308

Views

Showing that the image of a one dimensional representation is a subgroup of a cyclic group

Published on 11 Apr 2022 - 16:36

score 54 · Answer 4 · 2022-04-15 02:44:49

54

Views

Non-trivial generating sets for subgroups of finite cyclic groups

Published on 15 Apr 2022 - 2:44

score 685 · Answer 5 · 2022-04-15 17:01:32

685

Views

Let $G$ be a finite, abelian group, prime $p\mid |G|$ and $G$ contain $p-1$ elements order of $p$. Prove $G$ is cyclic.

Published on 15 Apr 2022 - 17:01

score 224 · Answer 6 · 2026-03-29 12:24:25

224

Views

Cyclic quotient group as a subgroup?

Published on 29 Mar 2026 - 12:24

score 74 · Answer 7 · 2022-05-06 03:35:15

74

Views

About generators of a cyclic group of finite order

Published on 06 May 2022 - 3:35

score 74 · Answer 8 · 2022-05-06 07:26:45

74

Views

Counting the number of elements of a particular order in $\mathbb{Z}_n$

Published on 06 May 2022 - 7:26

score 72 · Answer 9 · 2026-03-29 22:44:22

72

Views

Finding a basis for a free module

Published on 29 Mar 2026 - 22:44

score 42 · Answer 10 · 2022-05-09 19:56:27

42

Views

Cyclic subgroups of $(5)$

Published on 09 May 2022 - 19:56

score 46 · Answer 11 · 2022-05-11 19:27:01

46

Views

Is every normal subgroup of some group also a cyclic subgroup?

Published on 11 May 2022 - 19:27

score 98 · Answer 12 · 2022-05-15 19:47:19

98

Views

Is this conclusion from $⟨\alpha⟩=⟨\alpha^k⟩$?

Published on 15 May 2022 - 19:47

score 141 · Answer 13 · 2026-04-01 01:26:48

141

Views

How to show that two groups are not isomorphic.

Published on 01 Apr 2026 - 1:26

score 1.2k · Answer 14 · 2022-05-19 20:52:47

1.2k

Views

Prove the number of elements of order $n$ in $\mathbb{Z}_n$ is $\phi (n)$

Published on 19 May 2022 - 20:52

score 1k · Answer 15 · 2022-05-25 20:34:31

1k

Views

Suppose $G$ is a group and $H$ and $K$ are subgroups of $G$ such that $|H|=39$ and $|K|=65$. Prove that $H \cap K$ is cyclic.

Published on 25 May 2022 - 20:34

List Question

If G is a group, $H< G^{|G|}$ and $|H|\geq 2^{|G|}$, then can $H$ be cyclic?

Proof that if $G$ is a group with no proper subgroups and order $>1$, then $G$ is cyclic with prime order

Showing that the image of a one dimensional representation is a subgroup of a cyclic group

Non-trivial generating sets for subgroups of finite cyclic groups

Let $G$ be a finite, abelian group, prime $p\mid |G|$ and $G$ contain $p-1$ elements order of $p$. Prove $G$ is cyclic.

Cyclic quotient group as a subgroup?

About generators of a cyclic group of finite order

Counting the number of elements of a particular order in $\mathbb{Z}_n$

Finding a basis for a free module

Cyclic subgroups of $(5)$

Is every normal subgroup of some group also a cyclic subgroup?

Is this conclusion from $⟨\alpha⟩=⟨\alpha^k⟩$?

How to show that two groups are not isomorphic.

Prove the number of elements of order $n$ in $\mathbb{Z}_n$ is $\phi (n)$

Suppose $G$ is a group and $H$ and $K$ are subgroups of $G$ such that $|H|=39$ and $|K|=65$. Prove that $H \cap K$ is cyclic.

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