Units of group rings, the Bogomolov multiplier and the fake degree conjecture

作者：Garcia Rodriguez Javier^*; Jaikin Zapirain Andrei; Jezernik Urban

来源：Mathematical Proceedings of the Cambridge Philosophical Society, 2017, 163(1): 115-123.

DOI：10.1017/S0305004116000748

Let pi be a finite p-group and F-q a finite field with q = p(n) elements. Denote by I-Fq the augmentation ideal of the group ring F-q [pi]. We have found a surprising relation between the abelianization of 1+I-Fq, the Bogomolov multiplier B-0(pi) of p and the number of conjugacy classes k(pi) of pi:
vertical bar(1+I-Fq)(ab)vertical bar = q(k(pi)-1)vertical bar B-0(pi)vertical bar.
In particular, if pi is a finite p-group with a non-trivial Bogomolov multiplier, then 1 + I-Fq is a counterexample to the fake degree conjecture proposed by M. Isaacs.

• 出版日期2017-7