Question

If $H$ and $K$ are normal subgroups of $G$ and $H\bigcap K = \{e\}$, prove that $G$ is isomorphic to a subgroup of $G/H \times G/K$

score 3.9k · Answer 1 · 2018-10-21 06:28:36

3.9k

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If $H$ and $K$ are normal subgroups of $G$ and $H\bigcap K = \{e\}$, prove that $G$ is isomorphic to a subgroup of $G/H \times G/K$

Published on 21 Oct 2018 - 6:28

score 48 · Answer 2 · 2026-03-25 12:51:00

48

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Let $K \subseteq G$. Nec. and suff. cond. for that $\exists$ a normal subgr $H$ of $G$ s.t $exists$ transversal $I$ s.t $I \subseteq K$.

Published on 25 Mar 2026 - 12:51

score 101 · Answer 3 · 2026-03-25 12:50:57

101

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Intuitive explanation for: let $I_G$ be the group of > all inner automorphisms of $G$. Then $I_g$ is isomorphic to $G/C_G$

Published on 25 Mar 2026 - 12:50

score 78 · Answer 4 · 2018-10-24 10:00:40

78

Views

Find normal subgroup of the following group

Published on 24 Oct 2018 - 10:00

score 540 · Answer 5 · 2026-03-25 09:29:06

540

Views

Show that a non-abelian group of order 8 with a single element of order 2 is isomorphic to Q group

Published on 25 Mar 2026 - 9:29

score 146 · Answer 6 · 2018-10-31 12:11:13

146

Views

Proof that $\langle y\rangle$ is a normal subgroup of $G$ with order $q$ and $|G|=pq$ with $p$,$q$ prime

Published on 31 Oct 2018 - 12:11

score 56 · Answer 7 · 2026-03-25 11:16:23

56

Views

Are two lifts of a generator of a cyclic quotient conjugated?

Published on 25 Mar 2026 - 11:16

score 59 · Answer 8 · 2018-11-01 22:39:22

59

Views

Equivalent to subgroup being normal

Published on 01 Nov 2018 - 22:39

score 56 · Answer 9 · 2026-03-25 09:39:47

56

Views

Existence of normal subgroup of group with given property

Published on 25 Mar 2026 - 9:39

score 459 · Answer 10 · 2026-03-25 06:07:02

459

Views

What's an example of a finite, non-abelian, non-simple group that is not semidirectly reducible?

Published on 25 Mar 2026 - 6:07

score 137 · Answer 11 · 2026-03-25 17:35:24

137

Views

Normal subgroup generated by $D_8$

Published on 25 Mar 2026 - 17:35

score 43 · Answer 12 · 2018-11-09 05:47:45

43

Views

Using the first isomorphism theorem to prove subgroups

Published on 09 Nov 2018 - 5:47

score 65 · Answer 13 · 2018-11-09 17:13:21

65

Views

relation of certain definitions for groups

Published on 09 Nov 2018 - 17:13

score 34 · Answer 14 · 2018-11-10 00:56:41

34

Views

Showing that a conjugacy class is completely contained in a normal subgroup

Published on 10 Nov 2018 - 0:56

score 479 · Answer 15 · 2018-11-10 03:14:17

479

Views

Normal subgroups are not transitive, but $H \subseteq N \lhd G, H \lhd G \implies H \lhd N$?

Published on 10 Nov 2018 - 3:14

List Question

If $H$ and $K$ are normal subgroups of $G$ and $H\bigcap K = \{e\}$, prove that $G$ is isomorphic to a subgroup of $G/H \times G/K$

Let $K \subseteq G$. Nec. and suff. cond. for that $\exists$ a normal subgr $H$ of $G$ s.t $exists$ transversal $I$ s.t $I \subseteq K$.

Intuitive explanation for: let $I_G$ be the group of > all inner automorphisms of $G$. Then $I_g$ is isomorphic to $G/C_G$

Find normal subgroup of the following group

Show that a non-abelian group of order 8 with a single element of order 2 is isomorphic to Q group

Proof that $\langle y\rangle$ is a normal subgroup of $G$ with order $q$ and $|G|=pq$ with $p$,$q$ prime

Are two lifts of a generator of a cyclic quotient conjugated?

Equivalent to subgroup being normal

Existence of normal subgroup of group with given property

What's an example of a finite, non-abelian, non-simple group that is not semidirectly reducible?

Normal subgroup generated by $D_8$

Using the first isomorphism theorem to prove subgroups

relation of certain definitions for groups

Showing that a conjugacy class is completely contained in a normal subgroup

Normal subgroups are not transitive, but $H \subseteq N \lhd G, H \lhd G \implies H \lhd N$?

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