Question

Show $N$ is a normal subgroup of $G$ where $G$ is a subgroup of $GL_{2}(\mathbb{Q}).$

score 164 · Answer 1 · 2019-05-23 08:51:46

164

Views

Show $N$ is a normal subgroup of $G$ where $G$ is a subgroup of $GL_{2}(\mathbb{Q}).$

Published on 23 May 2019 - 8:51

score 46 · Answer 2 · 2019-05-26 15:28:22

46

Views

Show a group $G$ of invertible $2 \times 2$ matrices with coefficients modulo $13$ has seven subclasses and prove it has 3 normal subgroups.

Published on 26 May 2019 - 15:28

score 1k · Answer 3 · 2019-06-05 13:44:30

1k

Views

For a group whose order is the product of two distinct primes, What is the order of the center of the group?

Published on 05 Jun 2019 - 13:44

score 94 · Answer 4 · 2026-03-25 12:52:57

94

Views

Does $\Sigma$ generate the variety of all groups?

Published on 25 Mar 2026 - 12:52

score 149 · Answer 5 · 2026-03-25 19:07:13

149

Views

Let $G$ be a group of order $8$ and $y$ be an element of $G$ of order $4$. Prove that $y^2 \in Z(G)$

Published on 25 Mar 2026 - 19:07

score 89 · Answer 6 · 2026-03-25 23:38:21

89

Views

Lower bounds on the number of subgroups of a specific group

Published on 25 Mar 2026 - 23:38

score 613 · Answer 7 · 2019-06-11 10:34:15

613

Views

For $H,K \triangleleft G$ and $H\cap K=\{1\}$ show $hk=kh \ \forall k \in K, h\in H$

Published on 11 Jun 2019 - 10:34

score 33 · Answer 8 · 2026-03-25 20:40:03

33

Views

Subgroup automorphisms

Published on 25 Mar 2026 - 20:40

score 1k · Answer 9 · 2026-03-26 01:16:00

1k

Views

Topics in Algebra - N. Herstein Exercise from Section 2.12, Question 16 (Page 103)

Published on 26 Mar 2026 - 1:16

score 63 · Answer 10 · 2019-06-20 17:28:31

63

Views

Subgroup of order $10$ must be normal?

Published on 20 Jun 2019 - 17:28

score 4.6k · Answer 11 · 2026-03-25 20:36:21

4.6k

Views

Find all Quotient (or Factor) Groups of $D_4$ (Dihedral Group of order $8$)

Published on 25 Mar 2026 - 20:36

score 333 · Answer 12 · 2019-06-23 16:45:07

333

Views

Are the only single element normal subgroups precisely the elements that make up the center of a group?

Published on 23 Jun 2019 - 16:45

score 58 · Answer 13 · 2026-03-25 23:42:24

58

Views

$H\lhd G$, $|H|=p^k$ then $H$ is included in every $p$-Sylow subgroup of $G$

Published on 25 Mar 2026 - 23:42

score 36 · Answer 14 · 2019-06-24 19:48:24

36

Views

Trouble computing an index

Published on 24 Jun 2019 - 19:48

score 131 · Answer 15 · 2019-06-24 22:26:35

131

Views

Generalization of normal subgroup

Published on 24 Jun 2019 - 22:26

List Question

Show $N$ is a normal subgroup of $G$ where $G$ is a subgroup of $GL_{2}(\mathbb{Q}).$

Show a group $G$ of invertible $2 \times 2$ matrices with coefficients modulo $13$ has seven subclasses and prove it has 3 normal subgroups.

For a group whose order is the product of two distinct primes, What is the order of the center of the group?

Does $\Sigma$ generate the variety of all groups?

Let $G$ be a group of order $8$ and $y$ be an element of $G$ of order $4$. Prove that $y^2 \in Z(G)$

Lower bounds on the number of subgroups of a specific group

For $H,K \triangleleft G$ and $H\cap K=\{1\}$ show $hk=kh \ \forall k \in K, h\in H$

Subgroup automorphisms

Topics in Algebra - N. Herstein Exercise from Section 2.12, Question 16 (Page 103)

Subgroup of order $10$ must be normal?

Find all Quotient (or Factor) Groups of $D_4$ (Dihedral Group of order $8$)

Are the only single element normal subgroups precisely the elements that make up the center of a group?

$H\lhd G$, $|H|=p^k$ then $H$ is included in every $p$-Sylow subgroup of $G$

Trouble computing an index

Generalization of normal subgroup

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