Question

Can some finite group $G$ embed by conjugacy into $\operatorname{Sym}(H)$, for some $H \lhd G$?

score 78 · Answer 1 · 2019-11-15 11:08:28

78

Views

Can some finite group $G$ embed by conjugacy into $\operatorname{Sym}(H)$, for some $H \lhd G$?

Published on 15 Nov 2019 - 11:08

score 80 · Answer 2 · 2019-11-15 13:27:51

80

Views

$G$ finite group of order $n$. What's the least $l<n$ such that $G$ embeds in $S_l$?

Published on 15 Nov 2019 - 13:27

score 113 · Answer 3 · 2019-11-15 17:51:52

113

Views

Field Homomorphisms Equal to the Degree of $K$ Over $\mathbb{Q}$

Published on 15 Nov 2019 - 17:51

score 506 · Answer 4 · 2026-03-25 20:08:17

506

Views

Interpreting this problem from Dummit and Foote

Published on 25 Mar 2026 - 20:08

score 27 · Answer 5 · 2019-11-17 20:07:48

27

Views

Which subsets of the integers arise as the set of exponents of power endomorphisms for some group?

Published on 17 Nov 2019 - 20:07

score 60 · Answer 6 · 2019-11-21 07:37:09

60

Views

Probs 4 & 5, Sec 13, in Fraleigh's A FIRST COURSE IN ABSTRACT ALGEBRA, 7th ed: This map of $\mathbb{Z}_m$ to $\mathbb{Z}_n$ is a homomorphism iff ...?

Published on 21 Nov 2019 - 7:37

score 82 · Answer 7 · 2026-03-26 04:30:35

82

Views

Is there a homomorphism from $\mathbb R / \mathbb Q$ into the circle?

Published on 26 Mar 2026 - 4:30

score 43 · Answer 8 · 2026-03-26 12:51:31

43

Views

morphism between ordered field and integers

Published on 26 Mar 2026 - 12:51

score 81 · Answer 9 · 2026-02-23 04:00:34

81

Views

Is the preimage of a characteristic subgroup characteristic?

Published on 23 Feb 2026 - 4:00

score 89 · Answer 10 · 2019-11-23 11:15:23

89

Views

How many homomorphisms are there from $\mathbb D_5$ to $\mathbb A_4$?

Published on 23 Nov 2019 - 11:15

score 275 · Answer 11 · 2019-11-23 18:12:55

275

Views

Finding all group homomorphisms from $\mathbb{Z}/2\mathbb{Z} \times \mathbb{Z}/2\mathbb{Z} \times \mathbb{Z}/2\mathbb{Z} \to \mathbb{Z}/8\mathbb{Z}?$

Published on 23 Nov 2019 - 18:12

score 67 · Answer 12 · 2019-11-23 18:28:51

67

Views

Can a group homeomorphism $G\to Y$ have $Y\subsetneq G$?

Published on 23 Nov 2019 - 18:28

score 139 · Answer 13 · 2026-03-25 18:49:40

139

Views

What is the finest topology that makes $\lim_{n\to\infty} x+(1-2^{-6n})\cdot2^{\nu_2(x)}\cdot3^{\nu_3(x)-1}$ continuous?

Published on 25 Mar 2026 - 18:49

score 157 · Answer 14 · 2019-11-24 06:23:25

157

Views

Verifying Group Homomorphism Preserves Action on a Set

Published on 24 Nov 2019 - 6:23

score 809 · Answer 15 · 2019-11-25 23:29:09

809

Views

If $f:G \rightarrow G$ is a group homomorphism and $f(ab) = f(b)f(a)$ does this show that $f$ is NOT a homomorphism?

Published on 25 Nov 2019 - 23:29

List Question

Can some finite group $G$ embed by conjugacy into $\operatorname{Sym}(H)$, for some $H \lhd G$?

$G$ finite group of order $n$. What's the least $l<n$ such that $G$ embeds in $S_l$?

Field Homomorphisms Equal to the Degree of $K$ Over $\mathbb{Q}$

Interpreting this problem from Dummit and Foote

Which subsets of the integers arise as the set of exponents of power endomorphisms for some group?

Probs 4 & 5, Sec 13, in Fraleigh's A FIRST COURSE IN ABSTRACT ALGEBRA, 7th ed: This map of $\mathbb{Z}_m$ to $\mathbb{Z}_n$ is a homomorphism iff ...?

Is there a homomorphism from $\mathbb R / \mathbb Q$ into the circle?

morphism between ordered field and integers

Is the preimage of a characteristic subgroup characteristic?

How many homomorphisms are there from $\mathbb D_5$ to $\mathbb A_4$?

Finding all group homomorphisms from $\mathbb{Z}/2\mathbb{Z} \times \mathbb{Z}/2\mathbb{Z} \times \mathbb{Z}/2\mathbb{Z} \to \mathbb{Z}/8\mathbb{Z}?$

Can a group homeomorphism $G\to Y$ have $Y\subsetneq G$?

What is the finest topology that makes $\lim_{n\to\infty} x+(1-2^{-6n})\cdot2^{\nu_2(x)}\cdot3^{\nu_3(x)-1}$ continuous?

Verifying Group Homomorphism Preserves Action on a Set

If $f:G \rightarrow G$ is a group homomorphism and $f(ab) = f(b)f(a)$ does this show that $f$ is NOT a homomorphism?

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