TY - JOUR

T1 - Lie derived length and involutions in group algebras

AU - Balogh, Zsolt

N1 - Funding Information:
The author would like to thank the referee for the valuable comments and suggestions for clarifying the exposition. This research was supported by REA-NIH-OTKA-EU FP7 (Marie Curie action) co-funded grant No. MB08A-82343. This paper was written while the author was visiting the University College Dublin. He would like to gratefully acknowledge the kind hospitality from the host institution. The author thanks Thomas Unger for a careful reading of an earlier draft.

PY - 2012/6

Y1 - 2012/6

N2 - Let G be a group such that the set of p-elements of G forms a finite nonabelian subgroup, where p is an odd prime, and let F be a field of characteristic p. In this paper we prove that the lower bound of the Lie derived length of the group algebra FG given by Shalev in [11] is also a lower bound for the Lie derived length of the set of symmetric elements of FG for every involution which is linear extension of an involutive anti-automorphism of G. Furthermore, we provide counterexamples to the interesting cases which are not covered by the main theorem.

AB - Let G be a group such that the set of p-elements of G forms a finite nonabelian subgroup, where p is an odd prime, and let F be a field of characteristic p. In this paper we prove that the lower bound of the Lie derived length of the group algebra FG given by Shalev in [11] is also a lower bound for the Lie derived length of the set of symmetric elements of FG for every involution which is linear extension of an involutive anti-automorphism of G. Furthermore, we provide counterexamples to the interesting cases which are not covered by the main theorem.

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U2 - 10.1016/j.jpaa.2011.12.013

DO - 10.1016/j.jpaa.2011.12.013

M3 - Article

AN - SCOPUS:84857048907

VL - 216

SP - 1282

EP - 1287

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

SN - 0022-4049

IS - 6

ER -