Abstract In this paper, we study the number of conjugacy classes maximal cyclic subgroups a finite group

We prove a strong form of the Brumer–Stark Conjecture and, as a consequence, a strong form of Rubin’s integral refinement of the abelian Stark Conjecture, for a large class of abelian extensions of an arbitrary characteristic p global field k. This class includes all the abelian extensions K/k contained in the compositum kp∞ := kp · k∞ of the maximal pro-p abelian extension kp/k and the maximal...

Mixing in a natural way the notions of fully inert (see [6]) and strongly invariant (see [4]) subgroups of Abelian groups, we introduce the strongly inert subgroups which we determine for several classes of Abelian groups. Mathematics Subject Classification (2010). 20K27, 20K30, 20K10.

A string is Abelian square-free if it contains no Abelian squares; that is, adjacent substrings which are permutations of each other. An Abelian square-free string is maximal if it cannot be extended to the left or right by concatenating alphabet symbols without introducing an Abelian square. We construct Abelian square-free finite strings which are maximal by modifying a construction of Zimin....