List questions from finite-groups

Published on 19 Jun 2019 - 6:25

127

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Is there a group G of order 20 such that there exists a surjective homomorphism $\phi: G \rightarrow \mathbb{Z}_{15}$?

Published on 27 Mar 2026 - 5:03

137

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Subgroup of order 2 of a group of order 56

Published on 26 Mar 2026 - 1:16

74

Views

Some definition in finite group theory

Published on 21 Jun 2019 - 13:36

258

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Compute index of Fibonacci number mod prime

Published on 26 Mar 2026 - 16:06

94

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If $r = \frac{1}{|G|} \sum_{g \in G} \chi(g^{-1})g$, then $r^2 = 1/(\chi(1)) r$ in the group algebra

Published on 22 Jun 2019 - 13:48

155

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Why does $C_G(g)$ have index $q$ if $|G| = pq$ and $|g| = p$ for all nonidentity $g \in G$?

Published on 22 Jun 2019 - 14:31

94

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Getting real group representations from characters for a very small group (Order 12)

Published on 22 Jun 2019 - 20:25

104

Views

Sylow subgroup of a subgroup 5

Published on 28 Mar 2026 - 4:10

642

Views

Non-abelian finite $p$-group in which every element has prime order?

Published on 25 Mar 2026 - 12:51

56

Views

On the Sylow subgroups of a subgroup

Published on 26 Mar 2026 - 1:16

363

Views

Perfect finite groups with balanced presentations

Published on 25 Mar 2026 - 13:53

240

Views

If g and h are of same order in a finite group G, then there exists a group H, an extension of G such that g and h are conjugates in H .

Published on 25 Jun 2019 - 6:46

280

Views

Are all nilpotent groups hamiltonian?

Published on 25 Mar 2026 - 7:40

380

Views

Cyclic group of order 24

Published on 25 Jun 2019 - 10:31

List Question

How to show that a group homomorphism from $SL(2, \Bbb Z/n\Bbb Z)$ is one-to-one?

Is there a group G of order 20 such that there exists a surjective homomorphism $\phi: G \rightarrow \mathbb{Z}_{15}$?

Subgroup of order 2 of a group of order 56

Some definition in finite group theory

Compute index of Fibonacci number mod prime

If $r = \frac{1}{|G|} \sum_{g \in G} \chi(g^{-1})g$, then $r^2 = 1/(\chi(1)) r$ in the group algebra

Why does $C_G(g)$ have index $q$ if $|G| = pq$ and $|g| = p$ for all nonidentity $g \in G$?

Getting real group representations from characters for a very small group (Order 12)

Sylow subgroup of a subgroup 5

Non-abelian finite $p$-group in which every element has prime order?

On the Sylow subgroups of a subgroup

Perfect finite groups with balanced presentations

If g and h are of same order in a finite group G, then there exists a group H, an extension of G such that g and h are conjugates in H .

Are all nilpotent groups hamiltonian?

Cyclic group of order 24

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