关键词: principal ideal ring, extended group, linear group

Abstract: Suppose R is a principal ideal ring, R* is a multiplicative group which is composed of all reversible elements in R, and M_n(R),GL(n,R),SL(n,R) are denoted by, M_n(R)={A=(a_ij)_n×n|a_ij∈R,i,j=1,2,…,n},GL(n,R) = {g|g∈M_n(R),det_g∈R*},SL(n,R) = {g∈GL(n,R)|det_g=1},SL(n,R)≤G≤GL(n,R)(n≥3),respectively, then basing on these facts,this paper mainly focus on discussing all extended groups of Gr={(AB OD)∈G|A∈GL(r,R),(1≤r<n)} in G when R is a principal ideal ring. 

Key words: principal ideal ring, extended group, linear group