Central Extension Problem

Find a nontrivial central extension 1 --> Z_2 --> G --> A_4 --> 1 meaning determine a group G. Is it unique? (You may use the fact that A_4 has a normal series Z_2 x Z_2/Z3)

Composition Series

Write a composition series for the rotation group of the cube and show that it is indeed a composition series.

A basic property of a graph.

Show that a graph has at least two vertices with the same degree.

Nontrivial Central Extension

Find a nontrivial central Z_2 extension of the group A_4, meaning an extension of the form: 1 --> Z_2 --> G --> A_4 --> 1 Also, is it unique? The trivial extension is just the direct product of Z_2 and A_4.

Group properties of a set of infinite Teoplitz's matrixes are considered.

see attachment

Nonisomorphic Central Extensions

Describe all nonisomorphic central extensions of Z_2 x Z_2 by a cyclic group Z_n for arbitrary n, meaning central extensions of the form: 1 --> Z_n --> G --> Z_2 x Z_2 --> 1

Investigate the Automorphism Group of Z_p + Z_{p^2}

Investigate the Automorphism Group of Z_p + Z_{p^2}. Please see the attached file.

Extension of A_5

Extension of A_5

Conjugated Classes of Subgroups of A_5

List all Conjugated Classes of Subgroups of A_5

S_5 = Aut(A_5)

S_5 = Aut(A_5)