Question

Question to the proof of: Let $A$ be a finite abelian group and let $g \in A$. Suppose that $\chi(g)=1$ for every $\chi \in \hat A$. Then $g=1$.

score 299 · Answer 1 · 2026-03-28 11:32:49

299

Views

Question to the proof of: Let $A$ be a finite abelian group and let $g \in A$. Suppose that $\chi(g)=1$ for every $\chi \in \hat A$. Then $g=1$.

Published on 28 Mar 2026 - 11:32

score 106 · Answer 2 · 2016-04-30 13:06:31

106

Views

Can Lagrange's Theorem for algebraic structure apply here?

Published on 30 Apr 2016 - 13:06

score 480 · Answer 3 · 2016-04-30 23:44:56

Prove that for any n in $ \Bbb N $ there exists a unique cyclic subgroup $H_n$ $\subset$ G of order n. Where G is the group $\Bbb Q/$ $\Bbb Z$.

score 72 · Answer 4 · 2016-05-02 13:02:12

72

Views

Show that ${C_\infty }/\left\langle {{c^n}} \right\rangle \simeq {C_n}$

Published on 02 May 2016 - 13:02

score 311 · Answer 5 · 2026-02-23 15:12:31

311

Views

can composite groups have primitive roots (be cyclic)?

Published on 23 Feb 2026 - 15:12

score 383 · Answer 6 · 2016-05-05 13:19:52

383

Views

Generators of two groups with prime order $p$ already induce all the generators of the product group $G \times H$

Published on 05 May 2016 - 13:19

score 39 · Answer 7 · 2016-05-06 02:52:45

39

Views

Prove that if $H \cong \mathbb Z$ or $H \cong \mathbb Z_n$ then $H = ⟨g⟩$ for some $g ∈ G$.

Published on 06 May 2016 - 2:52

score 1.5k · Answer 8 · 2026-03-26 20:39:34

1.5k

Views

Group of order $p^2$

Published on 26 Mar 2026 - 20:39

score 548 · Answer 9 · 2016-05-08 12:49:43

548

Views

The Group of Units in a Ring

Published on 08 May 2016 - 12:49

score 330 · Answer 10 · 2026-03-22 04:18:26

330

Views

Holomorph of Cyclic $p$-groups

Published on 22 Mar 2026 - 4:18

score 381 · Answer 11 · 2016-05-15 20:07:57

381

Views

How to show $2$ and $3$ are generators of the additive group $Z/(5)$.

Published on 15 May 2016 - 20:07

score 119 · Answer 12 · 2026-03-27 14:22:26

119

Views

Quotient of $G= \left\langle a, b \ \middle|\ a^4, b^2=a^4, aba=b \right\rangle$ by $\langle a^2 \rangle$

Published on 27 Mar 2026 - 14:22

score 56 · Answer 13 · 2016-05-16 05:57:21

56

Views

New to cyclic groups: A group $H$ is cyclic if every element of $H$ is an integral power of some single element of

Published on 16 May 2016 - 5:57

score 342 · Answer 14 · 2016-05-20 21:02:51

342

Views

Is $\mathbb{Z}_4 \times \mathbb{Z}_ {12} \times \mathbb{Z}_9$ cyclic?

Published on 20 May 2016 - 21:02

score 627 · Answer 15 · 2016-05-22 09:24:09

627

Views

If $ p\neq q$ are odd prime integers then $(\mathbb{Z}/ pq\mathbb{ Z})^*$ is not cyclic

Published on 22 May 2016 - 9:24

List Question

Question to the proof of: Let $A$ be a finite abelian group and let $g \in A$. Suppose that $\chi(g)=1$ for every $\chi \in \hat A$. Then $g=1$.

Can Lagrange's Theorem for algebraic structure apply here?

Prove that for any n in $ \Bbb N $ there exists a unique cyclic subgroup $H_n$ $\subset$ G of order n. Where G is the group $\Bbb Q/$ $\Bbb Z$.

Show that ${C_\infty }/\left\langle {{c^n}} \right\rangle \simeq {C_n}$

can composite groups have primitive roots (be cyclic)?

Generators of two groups with prime order $p$ already induce all the generators of the product group $G \times H$

Prove that if $H \cong \mathbb Z$ or $H \cong \mathbb Z_n$ then $H = ⟨g⟩$ for some $g ∈ G$.

Group of order $p^2$

The Group of Units in a Ring

Holomorph of Cyclic $p$-groups

How to show $2$ and $3$ are generators of the additive group $Z/(5)$.

Quotient of $G= \left\langle a, b \ \middle|\ a^4, b^2=a^4, aba=b \right\rangle$ by $\langle a^2 \rangle$

New to cyclic groups: A group $H$ is cyclic if every element of $H$ is an integral power of some single element of

Is $\mathbb{Z}_4 \times \mathbb{Z}_ {12} \times \mathbb{Z}_9$ cyclic?

If $ p\neq q$ are odd prime integers then $(\mathbb{Z}/ pq\mathbb{ Z})^*$ is not cyclic

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