[图书][B] Group identities on units and symmetric units of group rings

GT Lee - 2010 - books.google.com
Let FG be the group ring of a group G over a field F. Write U (FG) for the group of units of FG.
It is an important problem to determine the conditions under which U (FG) satisfies a group …

Lie derived length and involutions in group algebras

Z Balogh - Journal of Pure and Applied Algebra, 2012 - Elsevier
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 …

Lie identities on skew elements in group algebras

GT Lee, SK Sehgal, E Spinelli - Contemp. Math, 2015 - books.google.com
Let F be a field and G a group having an involution∗. Extend∗ to an involution of the group
ring, FG. We discuss recent results concerning Lie properties satisfied by the set of skew …

Lie solvable group algebras of derived length three in characteristic three

H Chandra, M Sahai - Journal of Algebra and Its Applications, 2012 - World Scientific
LIE SOLVABLE GROUP ALGEBRAS OF DERIVED LENGTH THREE IN CHARACTERISTIC
THREE Page 1 Journal of Algebra and Its Applications Vol. 11, No. 5 (2012) 1250098 (12 …

Nilpotency indices of symmetric elements of group algebras

Z Balogh, T Juhász - Communications in Algebra, 2012 - Taylor & Francis
Let G be a group and let F be a field of characteristic different from 2. Denote by (FG)+ the
set of symmetric elements and by U+(FG) the set of symmetric units of the group algebra FG …

Lie metabelian skew elements in group rings

GT Lee, E Spinelli - Glasgow Mathematical Journal, 2014 - cambridge.org
Let F be a field of characteristic p≠ 2 and G a group without 2-elements having an
involution∗. Extend the involution linearly to the group ring FG, and let (FG)− denote the set …

Skew-symmetric elements in nonlinear involutions in group rings

AP Raposo - Algebra Colloquium, 2015 - World Scientific
Given an involution in a group G, it can be extended in various ways to an involution in the
group ring RG, where R is a ring, not necessarily commutative. In this paper nonlinear …

[PDF][PDF] Conditions for groups whose group algebras have minimal Lie derived length

Z Balogh, T Juhász - Annales Mathematicae et Informaticae, 2010 - ami.uni-eszterhazy.hu
Conditions for groups whose group algebras have minimal Lie derived length Page 1 Annales
Mathematicae et Informaticae 37 (2010) pp. 13–20 http://ami.ektf.hu Conditions for groups …

COMMUTATOR IDENTITIES ON SYMMETRIC ELEMENTS OF GROUP ALGEBRAS

T Juhasz, E TÓTH - Journal of Algebra and Its Applications, 2013 - World Scientific
Let K be a field of odd characteristic p, and let G be the direct product of a finite p-group P≠
1 and a Hamiltonian 2-group. We show that the set of symmetric elements (KG)* of the group …

Lie nilpotency indices of symmetric elements under oriented involutions in group algebras

JH Castillo - arXiv preprint arXiv:1209.6256, 2012 - arxiv.org
Let $ G $ be a group and let $ F $ be a field of characteristic different from 2. Denote by
$(FG)^+ $ the set of symmetric elements and by $\mathcal {U}^+(FG) $ the set of symmetric …