ON NON-ABELIAN GROUPS OF ORDER 2^n, n >= 4 USING GAP

Abstract

For every natural number n ≥ 4 there are exactly 4 non-abelian groups (up to isomorphism) of order 2 n , with a subgroup of index 2. In this article, we are going to illustrate all of these groups properties and axioms using Groups, Algorithms and Programming GAP.

Permutable Subgroups of Groups of Order 16

“…The classification of all 2-generators non-abelian groups of order 2 n , n ≥ 4 is found in [2]. To classify both cases abelian and non-abelian groups of order 16, we will use David Clausen method [3], which based on considering the different cases for the order of the centre.…”