Bounds for the relative n-th nilpotency degree in compact groups

Details Bounds for the relative n-th nilpotency degree in compact groups Bounds for the relative n-th nilpotency degree in compact groups

2009-10-25

arxiv.org/abs/0910.4716v3

Asian-European Journal of Mathematics, Vol. 4, No. 3 (2011), 495-506

Mathematics

Group Theory

9 pages; to appear in Asian-European Journal of Mathematics with several improvements

Scientific paper

10.1142/S1793557111000411

The line of investigation of the present paper goes back to a classical work of W. H. Gustafson of the 1973, in which it is described the probability that two randomly chosen group elements commute. In the same work, he gave some bounds for this kind of probability, providing information on the group structure. We have recently obtained some generalizations of his results for finite groups. Here we improve them in the context of the compact groups.

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