Question

Proving there is a unique subgroup $H\le S_4$ isomorphic to $G=\langle (13),(23~~4)\rangle\le S_7.$

score 99 · Answer 1 · 2026-03-31 17:50:40

99

Views

Proving there is a unique subgroup $H\le S_4$ isomorphic to $G=\langle (13),(23~~4)\rangle\le S_7.$

Published on 31 Mar 2026 - 17:50

score 161 · Answer 2 · 2026-04-01 06:33:31

161

Views

Must two groups with all subgroups of the same order be isomorphic?

Published on 01 Apr 2026 - 6:33

score 92 · Answer 3 · 2026-03-27 04:21:49

92

Views

$H,K \leq G$, $|H| = 126, |K| = 228$. Show that $H \cap K \leq G$ is either cyclic or isomorphic to $D_3$

Published on 27 Mar 2026 - 4:21

score 78 · Answer 4 · 2023-10-07 17:49:03

78

Views

Show $f(x)=1/x$ and $g(x)=(x-1)/x$ produce a group of functions isomorphic to the symmetric group $S_3$ when binary operation is used as map.

Published on 07 Oct 2023 - 17:49

score 87 · Answer 5 · 2023-10-19 07:19:38

87

Views

Infinite group without a subgroup isomorphic to $\mathbb{Z}$?

Published on 19 Oct 2023 - 7:19

score 144 · Answer 6 · 2023-10-21 11:11:36

144

Views

Show there is no isomorphism between a subgroup of $ \mathbb{Q}$ and $\mathbb{Z} \times \mathbb{Z}$

Published on 21 Oct 2023 - 11:11

score 72 · Answer 7 · 2026-03-28 17:40:30

72

Views

Similar short exact sequences where the first abelian group is different

Published on 28 Mar 2026 - 17:40

score 62 · Answer 8 · 2026-03-26 17:34:31

62

Views

Is there any spin group $Spin(n)$ for any value of $n$ which is isomorphic to $SU(3)$?

Published on 26 Mar 2026 - 17:34

score 86 · Answer 9 · 2023-10-22 22:39:40

86

Views

The projective linear group $PGL_2(q)$ and $SL_2(q)$

Published on 22 Oct 2023 - 22:39

score 87 · Answer 10 · 2023-10-24 07:38:29

87

Views

Cantor-Schröder-Bernstein theorem for finitely generated abelian groups

Published on 24 Oct 2023 - 7:38

score 111 · Answer 11 · 2023-10-24 15:27:18

111

Views

Is $\mathbb{Q^{*}}$ under multiplication isomorphic to $\mathbb{Q^{+}}$ under multiplication?

Published on 24 Oct 2023 - 15:27

score 52 · Answer 12 · 2026-03-27 04:17:44

52

Views

Index of the multiple of a group in itself

Published on 27 Mar 2026 - 4:17

score 231 · Answer 13 · 2023-10-26 09:45:49

231

Views

Prove $k$ and $|G|$ is coprime when $\varphi_k(g)=g^k$ is a automorphism

Published on 26 Oct 2023 - 9:45

score 176 · Answer 14 · 2026-03-25 19:02:24

176

Views

When is general linear group isomorphic to special linear group?

Published on 25 Mar 2026 - 19:02

score 153 · Answer 15 · 2026-03-27 00:56:14

153

Views

Show that $G = HK$

Published on 27 Mar 2026 - 0:56

List Question

Proving there is a unique subgroup $H\le S_4$ isomorphic to $G=\langle (13),(23~~4)\rangle\le S_7.$

Must two groups with all subgroups of the same order be isomorphic?

$H,K \leq G$, $|H| = 126, |K| = 228$. Show that $H \cap K \leq G$ is either cyclic or isomorphic to $D_3$

Show $f(x)=1/x$ and $g(x)=(x-1)/x$ produce a group of functions isomorphic to the symmetric group $S_3$ when binary operation is used as map.

Infinite group without a subgroup isomorphic to $\mathbb{Z}$?

Show there is no isomorphism between a subgroup of $ \mathbb{Q}$ and $\mathbb{Z} \times \mathbb{Z}$

Similar short exact sequences where the first abelian group is different

Is there any spin group $Spin(n)$ for any value of $n$ which is isomorphic to $SU(3)$?

The projective linear group $PGL_2(q)$ and $SL_2(q)$

Cantor-Schröder-Bernstein theorem for finitely generated abelian groups

Is $\mathbb{Q^{*}}$ under multiplication isomorphic to $\mathbb{Q^{+}}$ under multiplication?

Index of the multiple of a group in itself

Prove $k$ and $|G|$ is coprime when $\varphi_k(g)=g^k$ is a automorphism

When is general linear group isomorphic to special linear group?

Show that $G = HK$

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