List questions from finite-groups

Published on 16 Apr 2026 - 14:49

190

Views

Every order $p$ subgroup is normal in $p$ group?

Published on 16 Apr 2026 - 15:43

56

Views

Need a subgroup of a group $G$ which is maximal in $G$ but not normal.

Published on 13 Apr 2026 - 3:49

599

Views

Classification of finite minimal non-cyclic group

Published on 13 Apr 2026 - 6:37

2k

Views

The dual of the dual of a group $G$ is isomorphic to $G$

Published on 14 Apr 2026 - 23:33

239

Views

Exercise on subgroup of a direct product

Published on 14 Apr 2026 - 11:53

1.7k

Views

$G$ is a $p$-group $\implies $ $G$ has a normal subgroup of $p^k \ \forall k$

Published on 16 Apr 2026 - 6:25

65

Views

finite cyclic simple groups can be generated by two elements

Published on 15 Apr 2026 - 8:34

71

Views

finite simple groups (non abelian ) can be genarated by two elements.

Published on 14 Apr 2026 - 19:34

960

Views

Proper subgroup of a finite $p$-group

Published on 14 Apr 2026 - 22:44

2k

Views

Induced trivial representation

Published on 08 Apr 2026 - 21:43

44

Views

Techniques for finding a complete set of relations for a finitely presented group

Published on 09 Apr 2026 - 13:45

102

Views

Factor group of a $p$-group

Published on 13 Apr 2026 - 17:18

85

Views

Order of a general element in the units group mod $2^k$

Published on 15 Apr 2026 - 4:17

41

Views

Commutativity among the elements in the quotient group $G$ and the ful group $H$ under homomorphism $H \overset{r}{\to} G$

Published on 14 Apr 2026 - 3:07

List Question

Let $G$ a finite group of order $m$ with identity element $e$. Show that $g^m=e,\forall g\in G$

Every order $p$ subgroup is normal in $p$ group?

Need a subgroup of a group $G$ which is maximal in $G$ but not normal.

Classification of finite minimal non-cyclic group

The dual of the dual of a group $G$ is isomorphic to $G$

Exercise on subgroup of a direct product

$G$ is a $p$-group $\implies $ $G$ has a normal subgroup of $p^k \ \forall k$

finite cyclic simple groups can be generated by two elements

finite simple groups (non abelian ) can be genarated by two elements.

Proper subgroup of a finite $p$-group

Induced trivial representation

Techniques for finding a complete set of relations for a finitely presented group

Factor group of a $p$-group

Order of a general element in the units group mod $2^k$

Commutativity among the elements in the quotient group $G$ and the ful group $H$ under homomorphism $H \overset{r}{\to} G$

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