On Unit Groups in Modular Group Algebras of Abelian Groups with Totally Projective Components

• 来源期刊: 代数集刊(英文版)
• 关键词: normed unit groups totally projective groups pure subgroups finitely gen-erated groups countable ascending unions
• 年，卷（期）: 2007,（3）
• 页码范围: 515-520
• 页数: 6页
• 语种: 英文

摘要

We prove that if the p-reduced abelian group G is a special countable extension of its totally projective p-component of torsion G p and R is a perfect commutative unitary ring of prime characteristic p,then the group S(G) of all normed p-units in the group algebra RG modulo Gp,that is,S(G)/Gp,is totally projective.Our result strengthens both classical results obtained by May and Hill-Ullery.