Question

Direct Sum vs. Direct Product vs. Tensor Product

score 43.8k · Answer 1 · 2015-06-22 14:10:51

43.8k

Views

Direct Sum vs. Direct Product vs. Tensor Product

Published on 22 Jun 2015 - 14:10

score 561 · Answer 2 · 2015-08-20 05:14:27

561

Views

If groups $G$ and $H$ act on $X$, does $G\times H$ act on $X$?

Published on 20 Aug 2015 - 5:14

score 78 · Answer 3 · 2015-08-24 14:45:31

78

Views

For any $n>1$ , $ Aut(\mathbb Z^n) \cong GL(n , \mathbb Z)$ ? And for any $m,n >1$ , $Aut(\mathbb Z_m ^n) \cong GL(n , \mathbb Z_m)$ ?

Published on 24 Aug 2015 - 14:45

score 283 · Answer 4 · 2015-08-25 20:00:42

283

Views

Composition of module homomorphisms and their kernels

Published on 25 Aug 2015 - 20:00

score 475 · Answer 5 · 2015-09-07 11:14:11

475

Views

(Yet another..) Sum vs Product.

Published on 07 Sep 2015 - 11:14

score 1.3k · Answer 6 · 2015-09-14 11:11:19

1.3k

Views

Direct Product of Groups and Group Actions

Published on 14 Sep 2015 - 11:11

score 1.9k · Answer 7 · 2015-09-21 09:29:34

1.9k

Views

Nonnormal subgroup of $Q_8 \times Z_4$

Published on 21 Sep 2015 - 9:29

score 192 · Answer 8 · 2015-10-08 14:21:04

192

Views

If $G$ is isomorphic to $H_1\times\cdots\times H_n$, $H_i$ subgroup of $G$, then is $G$ the internal direct product of $H_1\cdots H_n$?

Published on 08 Oct 2015 - 14:21

score 327 · Answer 9 · 2015-10-21 12:07:14

327

Views

Is there a slick way to test whether $\Bbb Z_{mn}\cong \Bbb Z_m\oplus \Bbb Z_n$?

Published on 21 Oct 2015 - 12:07

score 41.1k · Answer 10 · 2015-10-28 18:48:35

41.1k

Views

Structure of groups of order $pq$, where $p,q$ are distinct primes.

Published on 28 Oct 2015 - 18:48

score 1.6k · Answer 11 · 2015-11-08 17:36:13

1.6k

Views

Prove that $G \times H$ is cyclic $\iff$ $\gcd(m,n) =1$

Published on 08 Nov 2015 - 17:36

score 145 · Answer 12 · 2015-11-14 23:43:07

145

Views

Group Theory: let $G$ be a group and let $G=H\times K$, is it true that $G/H\cong K$?

Published on 14 Nov 2015 - 23:43

score 119 · Answer 13 · 2026-03-22 10:07:55

119

Views

Proving the direct product $S^3 \times \mathbb R^{+}$ is isomorphic to $H^{*}$

Published on 22 Mar 2026 - 10:07

score 2.5k · Answer 14 · 2015-11-29 13:30:19

2.5k

Views

Which of the following group is isomorphic to the group $S_3\times \mathbb Z_2$?

Published on 29 Nov 2015 - 13:30

score 670 · Answer 15 · 2015-11-30 00:01:56

670

Views

Determing the isomorphism class of $U(16)$ and writing it as an internal direct product of cyclic groups.

Published on 30 Nov 2015 - 0:01

List Question

Direct Sum vs. Direct Product vs. Tensor Product

If groups $G$ and $H$ act on $X$, does $G\times H$ act on $X$?

For any $n>1$ , $ Aut(\mathbb Z^n) \cong GL(n , \mathbb Z)$ ? And for any $m,n >1$ , $Aut(\mathbb Z_m ^n) \cong GL(n , \mathbb Z_m)$ ?

Composition of module homomorphisms and their kernels

(Yet another..) Sum vs Product.

Direct Product of Groups and Group Actions

Nonnormal subgroup of $Q_8 \times Z_4$

If $G$ is isomorphic to $H_1\times\cdots\times H_n$, $H_i$ subgroup of $G$, then is $G$ the internal direct product of $H_1\cdots H_n$?

Is there a slick way to test whether $\Bbb Z_{mn}\cong \Bbb Z_m\oplus \Bbb Z_n$?

Structure of groups of order $pq$, where $p,q$ are distinct primes.

Prove that $G \times H$ is cyclic $\iff$ $\gcd(m,n) =1$

Group Theory: let $G$ be a group and let $G=H\times K$, is it true that $G/H\cong K$?

Proving the direct product $S^3 \times \mathbb R^{+}$ is isomorphic to $H^{*}$

Which of the following group is isomorphic to the group $S_3\times \mathbb Z_2$?

Determing the isomorphism class of $U(16)$ and writing it as an internal direct product of cyclic groups.

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