List questions from cyclic-groups

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Determing the isomorphism class of $U(16)$ and writing it as an internal direct product of cyclic groups.

Published on 30 Nov 2015 - 0:01

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How to show $\frac{\mathbb{Z}_m\times \mathbb{Z}_n}{\langle (a,b)\rangle}\simeq \mathbb{Z}_{\frac mc}\times \mathbb{Z}_{\frac nd}$?

Published on 02 Dec 2015 - 9:01

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Abelian Groups and orders

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Abelian Group G and it's order (Let G be an abelian group, and let a∈G)

Published on 03 Dec 2015 - 0:46

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$G$ cyclic group of order $24$, and $H=\langle x^6\rangle$, find the order of each element of $G/H$

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What are the distinct cyclic subgroups of order 12 in $\mathbb{Z}_6 \times \mathbb{Z}_{10}^\times$?

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Is the group Z2 x Z9 cyclic?

Published on 07 Dec 2015 - 4:57

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Group of order $255$ is cyclic

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Prove the group transitivity of alternating group $A_n \quad n>2$?

Published on 08 Dec 2015 - 14:46

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Why group of order 6 has to have just two elements of order 3

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There does not exist group $G$ such that ${\rm Aut}(G)\cong \mathbb{Z}_n$ (for odd $n$)

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units of group ring $\mathbb{Q}(G)$ when $G$ is infinite and cyclic

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nth root of unity in a cyclic group $\mathbb{Z}_p^*$

Published on 29 Mar 2026 - 11:44

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Cyclic group given a group action

Published on 14 Dec 2015 - 14:32

List Question

Which of the following group is isomorphic to the group $S_3\times \mathbb Z_2$?

Determing the isomorphism class of $U(16)$ and writing it as an internal direct product of cyclic groups.

How to show $\frac{\mathbb{Z}_m\times \mathbb{Z}_n}{\langle (a,b)\rangle}\simeq \mathbb{Z}_{\frac mc}\times \mathbb{Z}_{\frac nd}$?

Abelian Groups and orders

Abelian Group G and it's order (Let G be an abelian group, and let a∈G)

$G$ cyclic group of order $24$, and $H=\langle x^6\rangle$, find the order of each element of $G/H$

What are the distinct cyclic subgroups of order 12 in $\mathbb{Z}_6 \times \mathbb{Z}_{10}^\times$?

Is the group Z2 x Z9 cyclic?

Group of order $255$ is cyclic

Prove the group transitivity of alternating group $A_n \quad n>2$?

Why group of order 6 has to have just two elements of order 3

There does not exist group $G$ such that ${\rm Aut}(G)\cong \mathbb{Z}_n$ (for odd $n$)

units of group ring $\mathbb{Q}(G)$ when $G$ is infinite and cyclic

nth root of unity in a cyclic group $\mathbb{Z}_p^*$

Cyclic group given a group action

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