Centralizer Near-rings, Matrix Near-rings and Cyclic p-Groups

• 来源期刊: 代数集刊（英文版）
• 关键词: centralizer near-rings matrix near-rings automorphism groups stabilizer subgroups cyclic p-groups
• 年，卷（期）: 2005,（4）
• 页码范围: 567-584
• 页数: 18页
• 语种: 英文

摘要

If G is a finite group and A is a group of automorphisms of G, then it is known that the matrix near-ring Mm(MA(G); G) is a subnear-ring of the centralizer near ring MA(Gm) for every m ≥2. Conditions are known under which Mm(MA(G); G) is a proper subnear-ring of MA(Gm), and if .A and G are abelian, then conditions are known which imply the equality Mm(MA(G); G) = MA(Gm). In this paper, we characterize the groups 4 of automorphisms of a cyclic p-group G for which this equality holds. We also show that for every group A of automorphisms of a cyclic p-group G, either all the nonzero orbits of G are of unique type or none of the orbits of G is of unique type if p is odd, and there is a third possibility if p = 2, namely precisely one of the orbits of G is of unique type.