Question

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

score 63 · Answer 1 · 2026-04-14 21:02:04

63

Views

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

Published on 14 Apr 2026 - 21:02

score 1.8k · Answer 2 · 2026-04-14 13:37:06

1.8k

Views

Automorphism of Direct Product $Z_3\times Z_3$

Published on 14 Apr 2026 - 13:37

score 1.1k · Answer 3 · 2026-05-03 03:58:47

1.1k

Views

Equivalence of Internal & External Direct Product

Published on 03 May 2026 - 3:58

score 473 · Answer 4 · 2026-04-14 13:30:46

473

Views

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

Published on 14 Apr 2026 - 13:30

score 55 · Answer 5 · 2026-04-12 22:59:39

55

Views

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

Published on 12 Apr 2026 - 22:59

score 113 · Answer 6 · 2026-05-10 11:42:08

113

Views

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

Published on 10 May 2026 - 11:42

score 172 · Answer 7 · 2026-04-17 00:30:53

172

Views

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

Published on 17 Apr 2026 - 0:30

score 108 · Answer 8 · 2026-04-13 05:50:50

108

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 13 Apr 2026 - 5:50

score 87 · Answer 9 · 2026-04-15 16:24:33

87

Views

Tensorproduct or direct product

Published on 15 Apr 2026 - 16:24

score 94 · Answer 10 · 2026-05-07 01:44:55

94

Views

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

Published on 07 May 2026 - 1:44

score 254 · Answer 11 · 2026-05-05 13:53:24

254

Views

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

Published on 05 May 2026 - 13:53

score 1k · Answer 12 · 2026-04-15 17:23:09

1k

Views

Isomorphism from inner direct product to external.

Published on 15 Apr 2026 - 17:23

score 34 · Answer 13 · 2026-05-05 12:45:49

34

Views

Dual terminology to "component function"?

Published on 05 May 2026 - 12:45

score 270 · Answer 14 · 2026-04-25 05:57:15

270

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 25 Apr 2026 - 5:57

score 170 · Answer 15 · 2026-04-12 23:59:44

170

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 12 Apr 2026 - 23:59

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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