List questions from cyclic-groups

Published on 20 Jan 2015 - 2:27

625

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Prove any group of order $185$ is cyclic.

Published on 29 Mar 2026 - 22:33

71

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Some subgroup of $GL_2(\mathbb{Q})$

Published on 23 Jan 2015 - 11:39

499

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Subgroup of $\Bbb {Z}_m \oplus \Bbb {Z}_n$ where $(m,n)=1$.

Published on 23 Jan 2015 - 12:45

351

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The elements of $\Bbb{Z}_{20}^{\times}$

Published on 23 Jan 2015 - 23:22

94

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question regarding group theory proof

Published on 25 Jan 2015 - 13:41

518

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Cyclic group generator and multiplicative identity of correspondng ring

Published on 29 Jan 2015 - 15:54

1.1k

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$r$-cycle to a power $k$ is also an $r$-cycle if and only if $\gcd(k, r) = 1$

Published on 30 Jan 2015 - 20:24

1.1k

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give an example of a cyclic group with 6 generators.

Published on 02 Feb 2015 - 20:53

5.1k

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Show that a group that has only a finite number of subgroups must be a finite group

Published on 04 Feb 2015 - 5:20

354

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If |G|>1 is not prime, there exists a subgroup of G which is not G or {e}

Published on 04 Feb 2015 - 17:43

473

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Non-Cyclic Subgroup of $GL(2, \mathbb Z)$

Published on 06 Feb 2015 - 7:01

328

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$F$ a field and $G$ finite subset of $F \setminus \{0\}$ with 1 & satisfying $a, b ∈ G$ then $ab^{−1} ∈ G$. Show that $G$ is cyclic

Published on 10 Feb 2015 - 0:02

595

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Aut($C_p) = C_{p-1}$when $p$ is prime, why?

Published on 14 Feb 2015 - 16:22

1.8k

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A cyclic group of order $n$ can be generated by $a^k$ if $(k,n)=1$

Published on 14 Feb 2015 - 23:15

List Question

Is the group $G =\{a+b\sqrt{2}|a,b \in \mathbb{Z}\}$ cyclic?

Prove any group of order $185$ is cyclic.

Some subgroup of $GL_2(\mathbb{Q})$

Subgroup of $\Bbb {Z}_m \oplus \Bbb {Z}_n$ where $(m,n)=1$.

The elements of $\Bbb{Z}_{20}^{\times}$

question regarding group theory proof

Cyclic group generator and multiplicative identity of correspondng ring

$r$-cycle to a power $k$ is also an $r$-cycle if and only if $\gcd(k, r) = 1$

give an example of a cyclic group with 6 generators.

Show that a group that has only a finite number of subgroups must be a finite group

If |G|>1 is not prime, there exists a subgroup of G which is not G or {e}

Non-Cyclic Subgroup of $GL(2, \mathbb Z)$

$F$ a field and $G$ finite subset of $F \setminus \{0\}$ with 1 & satisfying $a, b ∈ G$ then $ab^{−1} ∈ G$. Show that $G$ is cyclic

Aut($C_p) = C_{p-1}$when $p$ is prime, why?

A cyclic group of order $n$ can be generated by $a^k$ if $(k,n)=1$

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