Identifying long cycles in finite alternating and symmetric groups acting on subsets

Comparison of pregnancy outcomes of frozen embryo transfers in women undergoing artificial endometrial preparation with and without short and long-acting gonadotropin releasing hormone agonists

Background & aim: There are conflicting results regarding the benefit of gonadotropin releasing hormone (GnRH) agonist treatment on frozen embryo transfer (FET) outcome. No study was found to compare pregnancy outcome between patients undergoing short and long acting types of GnRH agonist for FET cycles. This study aimed to assess the effectiveness of short and long ac...

Finite Groups with p-Sylow Coverings

Fuchsian groups, coverings of Riemann surfaces, subgroup growth, random quotients and random walks

Fuchsian groups (acting as isometries of the hyperbolic plane) occur naturally in geometry, combinatorial group theory, and other contexts. We use character-theoretic and probabilistic methods to study the spaces of homomorphisms from Fuchsian groups to symmetric groups. We obtain a wide variety of applications, ranging from counting branched coverings of Riemann surfaces, to subgroup growth an...

Arbitrary groups as two-point stabilisers of symmetric groups acting on partitions

We give a short, direct proof that given any finite group G there exist positive integers k and l and partitions α1 and α2 of {1, . . . , kl} into l subsets of size k such that (Skl)α1,α2 ∼= G. The method used will also show that given any finite group G there exists a regular bipartite graph whose automorphism group is isomorphic to G.

Monochrome Symmetric Subsets in Colorings of Finite Abelian Groups

A subset S of a group G is symmetric if there is an element g ∈ G such that gS−1g = S. We study some Ramsey type functions for symmetric subsets in finite Abelian groups.