Bogomolov Multipliers of Groups of Order 128

Abstract

This note describes an algorithm for computing Bogomolov multipliers of finite solvable groups. Compared to the existing algorithms, this one has improved performance and is able to recognize the commutator relations of the group that constitute its Bogomolov multiplier. As a sample case, we use the algorithm to effectively determine the multipliers of groups of order 128. Our results are a continuation of work of Chu et al. on Bogomolov multipliers of groups of order 64. In this paper, we utilize one of the key steps of another paper by the authors dealing with probabilistic aspects of universal commutator relations.

2000 AMS Subject Classification::

• 13A50
• 14E08
• 14M20
• 12F12

Keywords:

• Bogomolov multiplier
• groups of order 128