Question

Proving $P$ is a Sylow $p$-group of $PN$

score 82 · Answer 1 · 2026-03-25 22:26:36

82

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Proving $P$ is a Sylow $p$-group of $PN$

Published on 25 Mar 2026 - 22:26

score 1.5k · Answer 2 · 2026-03-30 16:59:46

1.5k

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Finding the elements with order $30$ in group $\mathbb Z^*_{31}$.

Published on 30 Mar 2026 - 16:59

score 100 · Answer 3 · 2026-03-28 07:51:38

100

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Kernel of homomorphism/Normal Subgroup for nxn matrices under multiplication

Published on 28 Mar 2026 - 7:51

score 486 · Answer 4 · 2026-04-12 10:40:56

486

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Is a reducible representation of a finite group always completely reducible?

Published on 12 Apr 2026 - 10:40

score 66 · Answer 5 · 2020-04-07 10:25:26

66

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how to verify that a set of matrices forms a group under multiplication?

Published on 07 Apr 2020 - 10:25

score 75 · Answer 6 · 2020-04-07 17:16:43

75

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Inclusions of representation rings $R(C_3;\mathbb{C})\hookrightarrow R(C_3;\mathbb{H})$

Published on 07 Apr 2020 - 17:16

score 38 · Answer 7 · 2020-04-08 10:18:03

38

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Classification of Groups of orders < 8: Prove that a group G with order 1 is isomorphic to the empty set.

Published on 08 Apr 2020 - 10:18

score 46 · Answer 8 · 2026-03-25 21:54:03

46

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Given a group $G$ of order $6$ and $a,b\in G$ with $|a|=3$ and $|b|=2$, show that the elements of $G$ are unique.

Published on 25 Mar 2026 - 21:54

score 104 · Answer 9 · 2026-04-09 15:20:30

104

Views

Symplectic Forms on Abelian Groups

Published on 09 Apr 2026 - 15:20

score 137 · Answer 10 · 2026-03-26 07:35:21

137

Views

Let $χ$ be an irreducible character of finite group $G$. Prove $χ(e)^2\leq \big[G: Z(χ)\big]$ $\iff$ if $χ(g) = 0$ for all $g ∈ G\backslash Z(χ)$.

Published on 26 Mar 2026 - 7:35

score 42 · Answer 11 · 2020-04-09 06:52:10

42

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$H_1,H_2$ subgroups such that $|H_2|/|H_1|$ is a prime. There is no subgroups stricly between them.

Published on 09 Apr 2020 - 6:52

score 83 · Answer 12 · 2026-04-10 21:24:35

83

Views

What should be the mental process for quickly evaluating representative Sylow subgroups of $A_5$?

Published on 10 Apr 2026 - 21:24

score 57 · Answer 13 · 2026-04-12 04:34:47

57

Views

Elliptic curves over extension fields with Galois group the Monster

Published on 12 Apr 2026 - 4:34

score 59 · Answer 14 · 2026-04-12 05:39:32

59

Views

Finite subset is a finitely generated group proposition

Published on 12 Apr 2026 - 5:39

score 35 · Answer 15 · 2026-03-26 06:30:16

35

Views

Order of cyclic group defined by presentation is finite

Published on 26 Mar 2026 - 6:30

List Question

Proving $P$ is a Sylow $p$-group of $PN$

Finding the elements with order $30$ in group $\mathbb Z^*_{31}$.

Kernel of homomorphism/Normal Subgroup for nxn matrices under multiplication

Is a reducible representation of a finite group always completely reducible?

how to verify that a set of matrices forms a group under multiplication?

Inclusions of representation rings $R(C_3;\mathbb{C})\hookrightarrow R(C_3;\mathbb{H})$

Classification of Groups of orders < 8: Prove that a group G with order 1 is isomorphic to the empty set.

Given a group $G$ of order $6$ and $a,b\in G$ with $|a|=3$ and $|b|=2$, show that the elements of $G$ are unique.

Symplectic Forms on Abelian Groups

Let $χ$ be an irreducible character of finite group $G$. Prove $χ(e)^2\leq \big[G: Z(χ)\big]$ $\iff$ if $χ(g) = 0$ for all $g ∈ G\backslash Z(χ)$.

$H_1,H_2$ subgroups such that $|H_2|/|H_1|$ is a prime. There is no subgroups stricly between them.

What should be the mental process for quickly evaluating representative Sylow subgroups of $A_5$?

Elliptic curves over extension fields with Galois group the Monster

Finite subset is a finitely generated group proposition

Order of cyclic group defined by presentation is finite

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