List questions from cyclic-groups

Published on 30 May 2020 - 9:23

146

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Cardinality of the kernel of multiplication map

Published on 03 Jun 2020 - 3:04

792

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Automorphism of commutative groups.

Published on 29 Mar 2026 - 16:49

389

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Quotient C8 by C2 group

Published on 04 Jun 2020 - 9:31

511

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Transforming a permutation into a rotation

Published on 26 Mar 2026 - 17:43

310

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If $G$ is a group with $|G|\ge2$ and has no subgroups except the two trivial ones, then $G$ is cyclic and of prime order.

Published on 07 Jun 2020 - 14:49

261

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Question from Mac Lane and Birkoff (Chapter II, section 3, problem 9) -- $\operatorname{Aut} (\mathbb{Z}_6) \cong \mathbb{Z}_2$

Published on 29 Mar 2026 - 16:49

71

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Power of an element of a permutation

Published on 26 Mar 2026 - 16:05

149

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Explaination of proof of Property of cyclic subgroup.

Published on 10 Jun 2020 - 10:09

550

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Is the inverse of an element in a group different than the element (except for $e$)? Also, are all the subgroup of a cyclic group cyclic?

Published on 10 Jun 2020 - 16:15

93

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If $|A|=pq$ and $A\lhd B$ is a Nontrivial Normal Subgroup, the Quotient Group $A/B$ is Cyclic

Published on 26 Mar 2026 - 21:10

215

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Show that a cyclic group of order $n$ has $n-1$ generators iff $n$ is prime.

Published on 11 Jun 2020 - 11:48

136

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Show a code is cyclic given the generator matrix

Published on 28 Mar 2026 - 11:42

99

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Prove that $A/B$ is cyclic if and only if $\gcd(a,b,c,d) = 1$.

Published on 26 Mar 2026 - 8:14

54

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when $n=12$ and $k=7$, can we generate a sub-group?

Published on 22 Jun 2020 - 11:49

List Question

Groups of units of cyclic groups of order $2^n$

Cardinality of the kernel of multiplication map

Automorphism of commutative groups.

Quotient C8 by C2 group

Transforming a permutation into a rotation

If $G$ is a group with $|G|\ge2$ and has no subgroups except the two trivial ones, then $G$ is cyclic and of prime order.

Question from Mac Lane and Birkoff (Chapter II, section 3, problem 9) -- $\operatorname{Aut} (\mathbb{Z}_6) \cong \mathbb{Z}_2$

Power of an element of a permutation

Explaination of proof of Property of cyclic subgroup.

Is the inverse of an element in a group different than the element (except for $e$)? Also, are all the subgroup of a cyclic group cyclic?

If $|A|=pq$ and $A\lhd B$ is a Nontrivial Normal Subgroup, the Quotient Group $A/B$ is Cyclic

Show that a cyclic group of order $n$ has $n-1$ generators iff $n$ is prime.

Show a code is cyclic given the generator matrix

Prove that $A/B$ is cyclic if and only if $\gcd(a,b,c,d) = 1$.

when $n=12$ and $k=7$, can we generate a sub-group?

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