The Isomorphism Problem of Normalized Unit Groups of Group Algebras of a Class of Finite 2-groups  

作　　者：Yu Lei WANG He Guo LIU 

机构地区：[1]Department of Mathematics,He’nan University of Technology,Zhengzhou 450001,P.R.China [2]Department of Mathematics,Hainan University,Haikou 570228,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2023年第11期2275-2282,共8页数学学报（英文版）

基　　金：National Natural Science Foundation of China(Grant No.12171142)。

摘　　要：Let p be a prime and F_p be a finite field of p elements.Let F_(pG)denote the group algebra of the finite p-group G over the field F_(p)and V(F_(pG))denote the group of normalized units in F_(pG).Suppose that G and H are finite p-groups given by a central extension of the form 1→Z_(p)^(m)→G→Z_(p)×···×Z_(p)→1 and G'≌Z_(p),m≥1.Then V(F_(p)G)≌V(F_(p)H)if and only if G≌H.Balogh and Bovdi only solved the isomorphism problem when p is odd.In this paper,the case p=2 is determined.

关 键 词：isomorphism problem normalized unit Frattini subgroup finite 2-group 

分 类 号：O152.1[理学—数学]