Perfect Isometry Groups for Cyclic Groups of Prime Order

2016/10/26 by Pornrat Ruengrot, Ruengrot, Pornrat
Engineering · Mathematics · #20C20 #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Representation Theory (math.RT) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1610.08393

openalex publication_date 2016/10/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A perfect isometry is an important relation between blocks of finite groups as many information about blocks are preserved by it. If we consider the group of all perfect isometries between a block to itself then this gives another information about the block that is also preserved by a perfect isometry. The structure of this group depends on the block and can be fairly simple or extremely complicated. In this paper we study the perfect isometry group for the block of C_p, the cyclic group of prime order, and completely describe the structure of this group. The result shows that any self perfect isometry for C_p is essentially either induced by an element in Aut(C_p), or obtained by multiplication by one of its linear characters, or a composition of both.

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