Question

Showing that an isomorphism exists between $\Bbb Z$ and a subgroup of $\Bbb Z \times \Bbb Z$.

score 60 · Answer 1 · 2018-05-02 01:59:39

60

Views

Showing that an isomorphism exists between $\Bbb Z$ and a subgroup of $\Bbb Z \times \Bbb Z$.

Published on 02 May 2018 - 1:59

score 1.8k · Answer 2 · 2026-03-25 11:06:45

1.8k

Views

Automorphism of Direct Product $Z_3\times Z_3$

Published on 25 Mar 2026 - 11:06

score 1.1k · Answer 3 · 2026-03-22 06:36:04

1.1k

Views

Equivalence of Internal & External Direct Product

Published on 22 Mar 2026 - 6:36

score 470 · Answer 4 · 2018-05-06 07:00:33

470

Views

Example of Group that is not Internal direct product under weaker condition

Published on 06 May 2018 - 7:00

score 52 · Answer 5 · 2018-05-06 07:34:13

52

Views

Description of Center of group and Normalizer of elements in terms of Subgroup used in Direct product

Published on 06 May 2018 - 7:34

score 109 · Answer 6 · 2026-03-25 09:27:42

109

Views

Counting elements of order 6 in $D_{12} \times Z_2$

Published on 25 Mar 2026 - 9:27

score 168 · Answer 7 · 2018-05-28 18:28:56

168

Views

Does it really matter that $G$ must be a nonabelian group in one exercise from Hungerford’s algebra book?

Published on 28 May 2018 - 18:28

score 106 · Answer 8 · 2018-05-28 19:37:32

106

Views

a nonabelian group $G$ such that it is the internal direct product of $H,K$ with $N$ a normal subgroup in the center trivially intersecting $H,K$

Published on 28 May 2018 - 19:37

score 83 · Answer 9 · 2026-03-21 22:49:59

83

Views

Tensorproduct or direct product

Published on 21 Mar 2026 - 22:49

score 81 · Answer 10 · 2026-03-22 22:32:56

81

Views

How can we describe all maximal proper subgroups of $G \times G$

Published on 22 Mar 2026 - 22:32

score 250 · Answer 11 · 2018-06-14 11:13:56

250

Views

Why does the direct sum of infinitely many groups require only finitely many are nonzero?

Published on 14 Jun 2018 - 11:13

score 1k · Answer 12 · 2018-06-17 09:43:45

1k

Views

Isomorphism from inner direct product to external.

Published on 17 Jun 2018 - 9:43

score 30 · Answer 13 · 2026-03-22 09:47:37

30

Views

Dual terminology to "component function"?

Published on 22 Mar 2026 - 9:47

score 261 · Answer 14 · 2026-03-19 13:44:53

261

Views

Quotient of finite, nilpotent group by Frattini subgroup is isomorphic to product of quotients of Sylow subgroups by their respective Frattini groups.

Published on 19 Mar 2026 - 13:44

score 167 · Answer 15 · 2018-08-03 23:08:37

167

Views

Let $G\simeq N_1\times N_2$ while $N_i$ are normal subgroups of $G$. Then what can we say about those $N_i$?

Published on 03 Aug 2018 - 23:08

List Question

Showing that an isomorphism exists between $\Bbb Z$ and a subgroup of $\Bbb Z \times \Bbb Z$.

Automorphism of Direct Product $Z_3\times Z_3$

Equivalence of Internal & External Direct Product

Example of Group that is not Internal direct product under weaker condition

Description of Center of group and Normalizer of elements in terms of Subgroup used in Direct product

Counting elements of order 6 in $D_{12} \times Z_2$

Does it really matter that $G$ must be a nonabelian group in one exercise from Hungerford’s algebra book?

a nonabelian group $G$ such that it is the internal direct product of $H,K$ with $N$ a normal subgroup in the center trivially intersecting $H,K$

Tensorproduct or direct product

How can we describe all maximal proper subgroups of $G \times G$

Why does the direct sum of infinitely many groups require only finitely many are nonzero?

Isomorphism from inner direct product to external.

Dual terminology to "component function"?

Quotient of finite, nilpotent group by Frattini subgroup is isomorphic to product of quotients of Sylow subgroups by their respective Frattini groups.

Let $G\simeq N_1\times N_2$ while $N_i$ are normal subgroups of $G$. Then what can we say about those $N_i$?

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