List questions from finite-groups

Published on 30 Oct 2018 - 20:02

140

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$Hol(\Bbb Z_2 \times \Bbb Z_2)$

Published on 26 Mar 2026 - 4:30

72

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Finding the order of a presentation of a group

Published on 25 Mar 2026 - 6:05

385

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Let $G$ be a nilpotent group of class 3. Then for every $x ,y ,z$ in $G$, $[x,y,z][y,z,x][z,x,y]=1$.

Published on 27 Mar 2026 - 18:22

1.4k

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Let $\phi:\Bbb{Z}_{20} \to \Bbb{Z}_{20}$ be an automorphism and $\phi(5)=5$. What are the possibilities of $\phi(x)$?

Published on 25 Mar 2026 - 15:52

364

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Schur's Lemma and $Z(G)$

Published on 25 Mar 2026 - 7:49

58

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The dihedral group $D_8$ isn't Hamiltonian

Published on 25 Mar 2026 - 19:04

244

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Frattini subgroup of a subgroup

Published on 25 Mar 2026 - 3:01

208

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Let $G$ be a finite group. If $a = bab$, is it true that $b^{2} = e$

Published on 01 Nov 2018 - 3:51

37

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Supplement in finite groups

Published on 26 Mar 2026 - 20:58

174

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producing element of infinite order in direct product of quotient groups

Published on 25 Mar 2026 - 23:39

1.8k

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If $G$ is an Abelian group with odd order, then the product of all its elements is the identity.

Published on 02 Nov 2018 - 6:05

303

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If orbits of a group have size greater than 2, and if H stabilizes some element in the orbit, why is it [G:H]=Size of the orbit?

Published on 03 Nov 2018 - 19:26

42

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Homomorphisms: What am I missing here?

Published on 26 Mar 2026 - 1:27

977

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Every non-trivial finite solvable group has a normal subgroup of prime index

Published on 04 Nov 2018 - 7:44

List Question

Is a Subgroup Characteristic in its Normalizer?

$Hol(\Bbb Z_2 \times \Bbb Z_2)$

Finding the order of a presentation of a group

Let $G$ be a nilpotent group of class 3. Then for every $x ,y ,z$ in $G$, $[x,y,z][y,z,x][z,x,y]=1$.

Let $\phi:\Bbb{Z}_{20} \to \Bbb{Z}_{20}$ be an automorphism and $\phi(5)=5$. What are the possibilities of $\phi(x)$?

Schur's Lemma and $Z(G)$

The dihedral group $D_8$ isn't Hamiltonian

Frattini subgroup of a subgroup

Let $G$ be a finite group. If $a = bab$, is it true that $b^{2} = e$

Supplement in finite groups

producing element of infinite order in direct product of quotient groups

If $G$ is an Abelian group with odd order, then the product of all its elements is the identity.

If orbits of a group have size greater than 2, and if H stabilizes some element in the orbit, why is it [G:H]=Size of the orbit?

Homomorphisms: What am I missing here?

Every non-trivial finite solvable group has a normal subgroup of prime index

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