Finite solvable tidy Groups whose orders are divisible by two primes

Abstract

In this paper, we investigate finite solvable tidy groups. We classify the tidy $\{p,q\}$-groups. Combining this with a previous result, we are able to characterize the finite tidy solvable groups. Using this characterization, we bound the Fitting height of finite tidy solvable groups and we prove that the quotients of finite tidy solvable groups are tidy.