Nonunits of group algebras over the fours group

Author:

Abdollahi A.12,Zanjanian S. M.1

Affiliation:

1. Department of Mathematics, University of Isfahan, Isfahan 81746-73441, Iran

2. School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P. O. Box 19395-5746, Tehran, Iran

Abstract

The conjecture on units of group algebras of a torsion-free supersoluble group is saying that every unit is trivial, i.e. a product of a nonzero element of the field and an element of the group. This conjecture is still open and even in the slightly simple case of the fours group [Formula: see text], it is not yet known. The main result of this paper is to show that a wide range of elements of group algebra of [Formula: see text] are nonunit.

Funder

School of Mathematics, Institute for Research in Fundamental Sciences

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Algebra and Number Theory

Cited by 2 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Quotients of Passman Fours Group and Non-units of Their Group Algebras;Bulletin of the Iranian Mathematical Society;2020-11-20

2. Units of Group Algebras of the Fours Group;Bulletin of the Iranian Mathematical Society;2019-12-03

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