On the Normal Complement Problem of Finite Group Algebra

IF 0.5 Q3 MATHEMATICS Asian-European Journal of Mathematics Pub Date : 2023-10-05 DOI:10.1142/s1793557123502029

Diksha Upadhyay, Harish Chandra, Suchi Bhatt

引用次数: 0

Abstract

Let [Formula: see text] be a group, [Formula: see text] be a finite field with a positive characteristic [Formula: see text], then [Formula: see text] is the group algebra of a group [Formula: see text] over [Formula: see text] with a positive characteristic [Formula: see text]. In this paper, the normal complement problem on semisimple group algebra [Formula: see text] is examined. The normal complement problem of groups of order up to 16 in their corresponding unit groups [Formula: see text] has already been discussed. We have proved that up to isomorphism all the three non-abelian groups of order 18 and up to isomorphism all three non-abelian groups of order 20 do not have normal complement in their corresponding unit groups [Formula: see text].

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有限群代数的正规补问题

设[公式:见文]是一个群，[公式:见文]是一个具有正特征的有限域[公式:见文]，则[公式:见文]是一个群的群代数[公式:见文]除以具有正特征的[公式:见文]。本文研究了半单群代数[公式:见文]上的正规补问题。已讨论了16阶以下的群在其对应的单元群中的正常补问题[公式:见文]。我们证明了不同构的所有三个18阶的非阿贝尔群和不同构的所有三个20阶的非阿贝尔群在其对应的单位群中没有正规补[公式:见文]。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Asian-European Journal of Mathematics MATHEMATICS-

CiteScore

1.30

自引率

12.50%

发文量

169

期刊介绍： Asian-European Journal of Mathematics is an international journal which is devoted to original research in the field of pure and applied mathematics. The aim of the journal is to provide a medium by which new ideas can be discussed among researchers from diverse fields in mathematics. It publishes high quality research papers in the fields of contemporary pure and applied mathematics with a broad range of topics including algebra, analysis, topology, geometry, functional analysis, number theory, differential equations, operational research, combinatorics, theoretical statistics and probability, theoretical computer science and logic. Although the journal focuses on the original research articles, it also welcomes survey articles and short notes. All papers will be peer-reviewed within approximately four months.

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