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https://www.ias.ac.in/article/fulltext/pmsc/130/0007

Group ring; unitary subgroup; unit group; conjugacy class

Let $G = H \times A$ be a finite 2-group, where $H$ is a non-abelian group of order 8 and $A$ is an elementary abelian 2-group. We obtain a normal complement of $G$ in the normalized unit group $V(FG)$ and in the unitary subgroup $V_{\ast}(FG)$ over the field $F$ with 2 elements. Further, for a finite field $F$ of characteristic 2, we derive class size of elements of $V(FG)$. Moreover, we provide class representatives of $V_{\ast}(FH)$.

S KAUR¹ M KHAN¹

1. Department of Mathematics, Indian Institute of Technology Ropar, Nangal Road, Rupnagar 140 001, India

Published

10 January 2020

Manuscript received

8 May 2018

Manuscript revised

15 March 2019

Accepted

31 May 2019

Early published

Unedited version published online

Final version published online

9 January 2020