Czechoslovak Mathematical Journal, Vol. 67, No. 3, pp. 855-865, 2017
On the derived length of units in group algebra
Dishari Chaudhuri, Anupam Saikia
Received April 27, 2016. First published August 10, 2017
Abstract: Let $G$ be a finite group $G$, $K$ a field of characteristic $p\geq17$ and let $U$ be the group of units in $KG$. We show that if the derived length of $U$ does not exceed $4$, then $G$ must be abelian.
Keywords: group algebra; group of units; derived subgroup
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Affiliations: Dishari Chaudhuri, Anupam Saikia, Department of Mathematics, Indian Institute of Technology Guwahati, Near Doul Gobinda Road, Amingaon, Pin-781039, Guwahati, Assam, India, e-mail: firstname.lastname@example.org, email@example.com