Search found 375 matches
- Tue Nov 10, 2015 12:07 pm
- Forum: Algebraic Structures
- Topic: On group theory
- Replies: 2
- Views: 2998
Re: On group theory
Thank you mr.Demetres. Here is a more analytical solution about \(\displaystyle{\left(\rm{Aut}(V_{4}),\circ\right)\simeq \left(S_{3},\circ\right)}\) where \(\displaystyle{V_{4}=C_{2}\times C_{2}=\left\{e,a,b,c\right\}}\) is \(\displaystyle{\rm{Klein's}}\) group. Let \(\displaystyle{X=\left\{a,b,c\ri...
- Mon Nov 09, 2015 3:38 pm
- Forum: Algebraic Structures
- Topic: On group theory 4
- Replies: 1
- Views: 3012
On group theory 4
Find all the functions \(\displaystyle{f:\left(\mathbb{Z}_{6},+\right)\longrightarrow \left(S_{3},\circ\right)}\) having the property \(\displaystyle{f(x+y)=f(x)\circ f(y)\,,\forall\,x\,,y\in\mathbb{Z}_{6}\,\,\,\,\,\,}\) (homomorphism) .
- Mon Nov 09, 2015 3:37 pm
- Forum: Algebraic Structures
- Topic: On group theory 3
- Replies: 1
- Views: 2120
On group theory 3
Let \(\displaystyle{\left(G,\cdot\right)}\) be a group and \(\displaystyle{N}\) a normal subgroup of \(\displaystyle{\left(G,\cdot\right)}\), that is \(\displaystyle{N\trianglelefteq G}\) . Prove that there exists a subgroup \(\displaystyle{K}\) of the group \(\displaystyle{Z(G/N)}\) such that: \(\d...
- Mon Nov 09, 2015 3:36 pm
- Forum: Algebraic Structures
- Topic: On group theory 2
- Replies: 2
- Views: 3054
On group theory 2
Find all the non-isomorphic abelian groups of order \(\displaystyle{300}\) .
- Mon Nov 09, 2015 1:58 pm
- Forum: Algebraic Structures
- Topic: On group theory
- Replies: 2
- Views: 2998
On group theory
Let \(\displaystyle{\left(G,\cdot\right)}\) be a group such that the group \(\displaystyle{\left(\rm{Aut}(G),\circ\right)}\) is cyclic.
Prove that the group \(\displaystyle{\left(G,\cdot\right)}\) is an abelian group.
Is the converse true ?
Prove that the group \(\displaystyle{\left(G,\cdot\right)}\) is an abelian group.
Is the converse true ?