A note on normal complement problem for split metacyclic groups

Abstract

In this article, we discuss the normal complement problem for metacyclic groups in modular group algebras. If F is the field with p elements and G is a finite split metacyclic p-group of nilpotency class 2, then we prove that G has a normal complement in UðFGÞ: For a finite field F of characteristic p, where p is an odd prime, we prove that D2pm has a normal complement in UðFD2pm Þ if and only if p ¼ 3 and jFj ¼ 3:.