Resolvable Mendelsohn designs and finite Frobenius groups
Abstract
We prove the existence and give constructions of a -fold perfect resolvable -Mendelsohn design for any integers with such that there exists a finite Frobenius group whose kernel has order and whose complement contains an element of order , where is the least prime factor of . Such a design admits as a group of automorphisms and is perfect when is a prime. As an application we prove that for any integer in prime factorization, and any prime dividing for , there exists a resolvable perfect -Mendelsohn design that admits a Frobenius group as a group of automorphisms. We also prove that, if is even and divides for , then there are at least resolvable -Mendelsohn designs that admit a Frobenius group as a group of automorphisms, where is Euler's totient function.
Keywords
Cite
@article{arxiv.1307.7455,
title = {Resolvable Mendelsohn designs and finite Frobenius groups},
author = {D. F. Hsu and Sanming Zhou},
journal= {arXiv preprint arXiv:1307.7455},
year = {2018}
}
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Final version