Similarity problem over 𝑆𝐿(𝑛,𝑍_{𝑝})

Abstract

The question of conjugacy separability in S L ( n , Z ) SL(n,Z) leads to the conjugacy problem in S L ( n , Z p ) SL(n,{Z_p}) for various primes p p . We present a simple solution to the similarity problem over S L ( n , Z p ) SL(n,{Z_p}) , which solves the conjugacy problem as a special case.