Question

For $A,B \in \mathscr{M}_{2\times2}(\mathbb{Q}) $ of finite order, show that $AB$ has infinite order

score 619 · Answer 1 · 2019-01-02 15:30:14

619

Views

For $A,B \in \mathscr{M}_{2\times2}(\mathbb{Q}) $ of finite order, show that $AB$ has infinite order

Published on 02 Jan 2019 - 15:30

score 358 · Answer 2 · 2019-01-03 10:48:47

358

Views

Why $\mathbb{Z}_m \times \mathbb{Z}_n, \, \text{gcd}(m,n) >1$ isn't cyclic?

Published on 03 Jan 2019 - 10:48

score 1.5k · Answer 3 · 2019-01-03 17:16:20

1.5k

Views

Prove that a group with $3$ elements is cyclic?

Published on 03 Jan 2019 - 17:16

score 2.8k · Answer 4 · 2026-03-26 10:45:11

2.8k

Views

Classification of abelian groups of order 72, and subgroups of order 4

Published on 26 Mar 2026 - 10:45

score 64 · Answer 5 · 2019-01-04 16:50:58

64

Views

If $|G|=p^2$, $p$ prime and $G$ is not cyslic $G\cong \Bbb Z/p\Bbb Z\times \Bbb Z/p\Bbb Z $

Published on 04 Jan 2019 - 16:50

score 394 · Answer 6 · 2026-03-26 01:14:34

394

Views

Construct a non trivial homomorphism from $\mathbb{Z}_2\times\mathbb{Z}_4$ to $\mathbb{Z}_8$

Published on 26 Mar 2026 - 1:14

score 98 · Answer 7 · 2019-01-09 01:09:00

98

Views

Number Fields with Cyclic Galois Groups

Published on 09 Jan 2019 - 1:09

score 121 · Answer 8 · 2026-03-25 19:01:09

121

Views

Why does $a^p \equiv 1\ (\text {mod}\ q)$?

Published on 25 Mar 2026 - 19:01

score 3.6k · Answer 9 · 2026-03-26 12:08:28

3.6k

Views

An abelian group $G$ of order $35$ with $g^{35}=e$ for all $g\in G$ is cyclic.

Published on 26 Mar 2026 - 12:08

score 195 · Answer 10 · 2026-03-26 22:58:35

195

Views

Is this a counterexample?

Published on 26 Mar 2026 - 22:58

score 219 · Answer 11 · 2026-03-26 12:08:24

219

Views

Find all non-isomorphic abelian groups s.t. $|G| \leq 30$ and $g^{12}=1, \, \forall g\in G$

Published on 26 Mar 2026 - 12:08

score 4.4k · Answer 12 · 2019-01-17 21:27:37

4.4k

Views

Prove that a finite Abelian group $G$ is not cyclic if and only if it contains a subgroup isomorphic to $\mathbb{Z}_p\times\mathbb{Z}_p$

Published on 17 Jan 2019 - 21:27

score 395 · Answer 13 · 2019-01-18 10:55:41

395

Views

The number of solutions to $x^k = a$ over $G$ a finite cyclic group is $\gcd(k,|G|)$

Published on 18 Jan 2019 - 10:55

score 58 · Answer 14 · 2019-01-19 22:36:27

58

Views

Finding cyclic group $\mathbb{Z}_n^\times$ of prime order

Published on 19 Jan 2019 - 22:36

score 211 · Answer 15 · 2019-01-20 18:33:00

211

Views

Gallian's Exercise 4.76: a 2008 GRE practice exam question: "exactly two of $x^3$, $x^5$, and $x^9$ are equal, determine $\lvert x^{13}\rvert$".

Published on 20 Jan 2019 - 18:33

List Question

For $A,B \in \mathscr{M}_{2\times2}(\mathbb{Q}) $ of finite order, show that $AB$ has infinite order

Why $\mathbb{Z}_m \times \mathbb{Z}_n, \, \text{gcd}(m,n) >1$ isn't cyclic?

Prove that a group with $3$ elements is cyclic?

Classification of abelian groups of order 72, and subgroups of order 4

If $|G|=p^2$, $p$ prime and $G$ is not cyslic $G\cong \Bbb Z/p\Bbb Z\times \Bbb Z/p\Bbb Z $

Construct a non trivial homomorphism from $\mathbb{Z}_2\times\mathbb{Z}_4$ to $\mathbb{Z}_8$

Number Fields with Cyclic Galois Groups

Why does $a^p \equiv 1\ (\text {mod}\ q)$?

An abelian group $G$ of order $35$ with $g^{35}=e$ for all $g\in G$ is cyclic.

Is this a counterexample?

Find all non-isomorphic abelian groups s.t. $|G| \leq 30$ and $g^{12}=1, \, \forall g\in G$

Prove that a finite Abelian group $G$ is not cyclic if and only if it contains a subgroup isomorphic to $\mathbb{Z}_p\times\mathbb{Z}_p$

The number of solutions to $x^k = a$ over $G$ a finite cyclic group is $\gcd(k,|G|)$

Finding cyclic group $\mathbb{Z}_n^\times$ of prime order

Gallian's Exercise 4.76: a 2008 GRE practice exam question: "exactly two of $x^3$, $x^5$, and $x^9$ are equal, determine $\lvert x^{13}\rvert$".

Trending Questions

Popular # Hahtags

Popular Questions