List questions from finite-groups

Published on 30 Sep 2014 - 8:33

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Does a Group being Finite Imply that It Is Cyclic?

Published on 01 Apr 2026 - 3:11

144

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Why $( Z_3\rtimes Z_2)\times Z_2 \cong (Z_3\times Z_2)\rtimes Z_2$?

Published on 30 Sep 2014 - 21:09

78

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Equivalence classes of (2,3)-pairs in PSL(2,q)

Published on 25 Mar 2026 - 11:16

1k

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Proving that $a$ is a $p$-cycle

Published on 01 Oct 2014 - 11:29

48

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Can we find a finite abelian group $(A,+)$ such that $A⊂ℝ$

Published on 01 Oct 2014 - 14:33

261

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Cayley's theorem --- more than one isomorphism

Published on 01 Oct 2014 - 16:00

2.9k

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Proof that the order of any finite $p$-group is a power of $p$

Published on 01 Oct 2014 - 21:42

115

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Automorphic group of a cyclic group

Published on 02 Oct 2014 - 19:40

1.2k

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Basis of vector space invariant under group action (of symmetric group)

Published on 02 Oct 2014 - 19:51

3.7k

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Prove that no finite abelian group is divisible.

Published on 29 Mar 2026 - 2:12

1.1k

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Subgroup of an abelian group isomorphic to a given quotient group

Published on 29 Mar 2026 - 3:02

132

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Is a group always contained in a group that surjects onto its automorphism group?

Published on 26 Mar 2026 - 12:47

5k

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Suppose $G$ is a group with exactly $8$ elements of order $3$. How many subgroups of order $3$ does $G$ have?

Published on 05 Oct 2014 - 10:43

1.6k

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Show that the dihedral group $D_n$ is isomorphic to a matrix group where all entries in the matrix are in $\Bbb{Z}_n$.

Published on 05 Oct 2014 - 16:34

List Question

Maximal Subgroups in Groups of Order $p^k$

Does a Group being Finite Imply that It Is Cyclic?

Why $( Z_3\rtimes Z_2)\times Z_2 \cong (Z_3\times Z_2)\rtimes Z_2$?

Equivalence classes of (2,3)-pairs in PSL(2,q)

Proving that $a$ is a $p$-cycle

Can we find a finite abelian group $(A,+)$ such that $A⊂ℝ$

Cayley's theorem --- more than one isomorphism

Proof that the order of any finite $p$-group is a power of $p$

Automorphic group of a cyclic group

Basis of vector space invariant under group action (of symmetric group)

Prove that no finite abelian group is divisible.

Subgroup of an abelian group isomorphic to a given quotient group

Is a group always contained in a group that surjects onto its automorphism group?

Suppose $G$ is a group with exactly $8$ elements of order $3$. How many subgroups of order $3$ does $G$ have?

Show that the dihedral group $D_n$ is isomorphic to a matrix group where all entries in the matrix are in $\Bbb{Z}_n$.

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