Question

If $G$ is non-abelian, then $\operatorname{Inn}(G)$ is not a normal subgroup of the group of all bijective mappings $G \to G$

score 422 · Answer 1 · 2014-04-12 17:19:03

422

Views

If $G$ is non-abelian, then $\operatorname{Inn}(G)$ is not a normal subgroup of the group of all bijective mappings $G \to G$

Published on 12 Apr 2014 - 17:19

score 104 · Answer 2 · 2014-04-14 16:22:33

104

Views

Subset of elements of a given order in a group

Published on 14 Apr 2014 - 16:22

score 285 · Answer 3 · 2014-04-15 21:04:25

285

Views

Isomorphisms between finite abelian groups and cyclic groups

Published on 15 Apr 2014 - 21:04

score 128 · Answer 4 · 2014-04-17 14:42:44

128

Views

conjugacy classes and order of group

Published on 17 Apr 2014 - 14:42

score 127 · Answer 5 · 2014-04-18 21:10:04

127

Views

What is the definition of linearly independent subset of an abelian group?

Published on 18 Apr 2014 - 21:10

score 730 · Answer 6 · 2014-04-19 05:46:01

730

Views

Can we give of the fact that a group of order $9$ is abelian without using an argument involving the product of two cyclic groups of order $3$?

Published on 19 Apr 2014 - 5:46

score 367 · Answer 7 · 2014-04-19 15:34:21

367

Views

Determining the structure of the abelian group, integral matrix

Published on 19 Apr 2014 - 15:34

score 3.4k · Answer 8 · 2014-04-20 15:24:17

3.4k

Views

A finite abelian group that does not contain a subgroup isomorphic to $\mathbb Z_p\oplus\mathbb Z_p$, for any prime $p$, is cyclic.

Published on 20 Apr 2014 - 15:24

score 1.4k · Answer 9 · 2014-04-21 14:10:06

1.4k

Views

If the intersection of a normal subgroup and the derived group is $\{e\}$, show that $N$ is a subset of $Z(G)$.

Published on 21 Apr 2014 - 14:10

score 787 · Answer 10 · 2014-04-23 06:13:50

787

Views

Equivalence relation to make a group commutative

Published on 23 Apr 2014 - 6:13

score 588 · Answer 11 · 2014-04-23 10:41:04

588

Views

Classifying $\mathbb{Z}_{12} \times \mathbb{Z}_3 \times \mathbb{Z}_6/\langle(8,2,4)\rangle$

Published on 23 Apr 2014 - 10:41

score 3.6k · Answer 12 · 2014-04-23 13:07:51

3.6k

Views

Let $G$ be a finite abelian group and let $p$ be a prime that divides order of $G$. then $G$ has an element of order $p$

Published on 23 Apr 2014 - 13:07

score 97 · Answer 13 · 2014-04-23 18:43:47

97

Views

Be $G=\{ e,g_1,g_2,\ldots, g_n \}$, $|G|=n+1$. Suppose $G$ has a unique element of order $2$, say $g_1$. Show that $eg_1g_2\ldots g_n=g_1$.

Published on 23 Apr 2014 - 18:43

score 42 · Answer 14 · 2014-04-23 19:05:06

42

Views

Evidence about the group $\left ( (\mathbb{Z}/p\mathbb{Z})^*,\underset{p}{ \odot} \right )$

Published on 23 Apr 2014 - 19:05

score 60 · Answer 15 · 2014-04-24 04:42:29

60

Views

Prove that $U(m) = U_{m/n_1} (m) \times U_{m/n_1} (m) \times \cdots\times U_{m/n_k}$

Published on 24 Apr 2014 - 4:42

List Question

If $G$ is non-abelian, then $\operatorname{Inn}(G)$ is not a normal subgroup of the group of all bijective mappings $G \to G$

Subset of elements of a given order in a group

Isomorphisms between finite abelian groups and cyclic groups

conjugacy classes and order of group

What is the definition of linearly independent subset of an abelian group?

Can we give of the fact that a group of order $9$ is abelian without using an argument involving the product of two cyclic groups of order $3$?

Determining the structure of the abelian group, integral matrix

A finite abelian group that does not contain a subgroup isomorphic to $\mathbb Z_p\oplus\mathbb Z_p$, for any prime $p$, is cyclic.

If the intersection of a normal subgroup and the derived group is $\{e\}$, show that $N$ is a subset of $Z(G)$.

Equivalence relation to make a group commutative

Classifying $\mathbb{Z}_{12} \times \mathbb{Z}_3 \times \mathbb{Z}_6/\langle(8,2,4)\rangle$

Let $G$ be a finite abelian group and let $p$ be a prime that divides order of $G$. then $G$ has an element of order $p$

Be $G=\{ e,g_1,g_2,\ldots, g_n \}$, $|G|=n+1$. Suppose $G$ has a unique element of order $2$, say $g_1$. Show that $eg_1g_2\ldots g_n=g_1$.

Evidence about the group $\left ( (\mathbb{Z}/p\mathbb{Z})^*,\underset{p}{ \odot} \right )$

Prove that $U(m) = U_{m/n_1} (m) \times U_{m/n_1} (m) \times \cdots\times U_{m/n_k}$

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