Question

Show that the Möbius group is isomorphic to the quotient of $GL_2(\Bbb C)$ by its centre.

score 826 · Answer 1 · 2026-03-28 11:34:10

826

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Show that the Möbius group is isomorphic to the quotient of $GL_2(\Bbb C)$ by its centre.

Published on 28 Mar 2026 - 11:34

score 62 · Answer 2 · 2026-03-25 04:39:17

62

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heuristics for determing if cayley tales are isomorphic

Published on 25 Mar 2026 - 4:39

score 200 · Answer 3 · 2018-01-12 20:16:35

200

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(Dis)proving isomorphism between $U= \{ z \in \Bbb C \mid |z| = 1 \}$ and $\Bbb R$

Published on 12 Jan 2018 - 20:16

score 2.4k · Answer 4 · 2026-03-27 22:20:12

2.4k

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Finite group with isomorphic normal subgroups and non-isomorphic quotients?

Published on 27 Mar 2026 - 22:20

score 14k · Answer 5 · 2010-10-30 19:13:45

14k

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$|G|>2$ implies $G$ has non trivial automorphism

Published on 30 Oct 2010 - 19:13

score 10k · Answer 6 · 2011-04-18 08:57:34

10k

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Group of positive rationals under multiplication not isomorphic to group of rationals

Published on 18 Apr 2011 - 8:57

score 3.4k · Answer 7 · 2026-03-28 10:41:44

3.4k

Views

free groups: $F_X\cong F_Y\Rightarrow|X|=|Y|$

Published on 28 Mar 2026 - 10:41

score 6k · Answer 8 · 2026-03-27 22:11:29

6k

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Isomorphic quotient groups

Published on 27 Mar 2026 - 22:11

score 7.1k · Answer 9 · 2012-01-21 06:19:34

7.1k

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Prove that there only two groups of order 4 up to isomorphism

Published on 21 Jan 2012 - 6:19

score 5.3k · Answer 10 · 2026-03-29 12:11:14

5.3k

Views

Is there a simple proof of the fact that if free groups $F(S)$ and $F(S')$ are isomorphic, then $\operatorname{card}(S)=\operatorname{card}(S')?$

Published on 29 Mar 2026 - 12:11

score 835 · Answer 11 · 2012-03-07 07:49:07

835

Views

For $H \leq G$, showing that $N_G(H)/C_G(H) \leq \text{Aut}(H)$

Published on 07 Mar 2012 - 7:49

score 2.6k · Answer 12 · 2012-04-11 15:06:01

2.6k

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Theorem: the icosahedral group is isomorphic to the alternating group $A_5$ , need more explain

Published on 11 Apr 2012 - 15:06

score 16.7k · Answer 13 · 2026-04-02 08:33:05

16.7k

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$\operatorname{Aut}(\mathbb Z_n)$ is isomorphic to $U_n$.

Published on 02 Apr 2026 - 8:33

score 1.8k · Answer 14 · 2026-03-26 23:09:14

1.8k

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Prove that the group isomorphism $\mathbb{Z}^m \cong \mathbb{Z}^n$ implies that $m = n$

Published on 26 Mar 2026 - 23:09

score 4.3k · Answer 15 · 2026-04-05 23:01:36

4.3k

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Show that, for every $n$, $A_{n+2}$ has a subgroup isomorphic to $S_n$

Published on 05 Apr 2026 - 23:01

List Question

Show that the Möbius group is isomorphic to the quotient of $GL_2(\Bbb C)$ by its centre.

heuristics for determing if cayley tales are isomorphic

(Dis)proving isomorphism between $U= \{ z \in \Bbb C \mid |z| = 1 \}$ and $\Bbb R$

Finite group with isomorphic normal subgroups and non-isomorphic quotients?

$|G|>2$ implies $G$ has non trivial automorphism

Group of positive rationals under multiplication not isomorphic to group of rationals

free groups: $F_X\cong F_Y\Rightarrow|X|=|Y|$

Isomorphic quotient groups

Prove that there only two groups of order 4 up to isomorphism

Is there a simple proof of the fact that if free groups $F(S)$ and $F(S')$ are isomorphic, then $\operatorname{card}(S)=\operatorname{card}(S')?$

For $H \leq G$, showing that $N_G(H)/C_G(H) \leq \text{Aut}(H)$

Theorem: the icosahedral group is isomorphic to the alternating group $A_5$ , need more explain

$\operatorname{Aut}(\mathbb Z_n)$ is isomorphic to $U_n$.

Prove that the group isomorphism $\mathbb{Z}^m \cong \mathbb{Z}^n$ implies that $m = n$

Show that, for every $n$, $A_{n+2}$ has a subgroup isomorphic to $S_n$

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