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.

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