List questions from finite-groups

Published on 26 Mar 2026 - 19:37

129

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How to prove that semidirect product of $Z_{13}$ and $Z_3$ is non Abelian for a non-trivial homomorphism

Published on 25 Mar 2026 - 7:46

30

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$2$-factorizations of a $4$-regular graph

Published on 03 Dec 2018 - 5:39

179

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Trouble understanding semidirect product of $Z_3$ and $Z_{13}$

Published on 03 Dec 2018 - 6:30

120

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How can I prove that $G/M\cap N \cong M/(M\cap N) \times N/(M\cap N)$ where $M,N \triangleleft G$ and $M.N=G$?

Published on 03 Dec 2018 - 8:01

101

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Semi direct product of Quaternion group with cyclic group of order p.

Published on 25 Mar 2026 - 7:44

68

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Relation between odd order theorem and the fact that every polynomial of odd order has at least one root

Published on 25 Mar 2026 - 3:03

31

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Homomorphism and relative order questions

Published on 26 Mar 2026 - 6:27

145

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A visual subject in group theory

Published on 28 Mar 2026 - 20:56

182

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Prove the existence of homomorphism.

Published on 26 Mar 2026 - 1:14

48

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How to construct the homomorphism in semidirect product of $Z_3$ and $Z_{13}$?

Published on 25 Mar 2026 - 7:46

507

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Sylow $3$-subgroups of an order $180$ group

Published on 04 Dec 2018 - 6:49

66

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If $G'=G$, and suppose $N_G(P)$ is solvable for $P\subseteq G$, show that $ G$ is simple.

Published on 04 Dec 2018 - 9:13

340

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There are only two groups of order six, up to isomorphism: $\mathbb Z_6$ and $S_3$.

Published on 04 Dec 2018 - 9:32

159

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Hamiltonian decomposability of 4- regular graphs

Published on 25 Mar 2026 - 4:50

List Question

isomorphism of normal subgroup

How to prove that semidirect product of $Z_{13}$ and $Z_3$ is non Abelian for a non-trivial homomorphism

$2$-factorizations of a $4$-regular graph

Trouble understanding semidirect product of $Z_3$ and $Z_{13}$

How can I prove that $G/M\cap N \cong M/(M\cap N) \times N/(M\cap N)$ where $M,N \triangleleft G$ and $M.N=G$?

Semi direct product of Quaternion group with cyclic group of order p.

Relation between odd order theorem and the fact that every polynomial of odd order has at least one root

Homomorphism and relative order questions

A visual subject in group theory

Prove the existence of homomorphism.

How to construct the homomorphism in semidirect product of $Z_3$ and $Z_{13}$?

Sylow $3$-subgroups of an order $180$ group

If $G'=G$, and suppose $N_G(P)$ is solvable for $P\subseteq G$, show that $ G$ is simple.

There are only two groups of order six, up to isomorphism: $\mathbb Z_6$ and $S_3$.

Hamiltonian decomposability of 4- regular graphs

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