Coset representatives for permutation groups
All crossed products of two cyclic groups are explicitly described using generators and relations. A necessary and sufficient condition for an extension of a group by a group to be a cyclic group is given.
We study solvability of equations of the form in the groups of order automorphisms of archimedean-complete totally ordered groups of rank 2. We determine exactly which automorphisms of the unique abelian such group have square roots, and we describe all automorphisms of the general ones.
This note contains Sylow's theorem, Lagrange's theorem and Hall's theorem for finite Bruck loops. Moreover, we explore the subloop structure of finite Bruck loops.