An MI-group is an algebraic structure based on a generalization of the concept of a monoid that satisfies the cancellation laws and is endowed with an invertible anti-automorphism representing inversion. In this paper, a topology is defined on an MI-group $G$ under which $G$ is  a topological MI-group. Then we will identify open, discrete and compact MI-subgroups. The connected components of th...

Most of the maximal subgroups of the Monster are now known, but in many cases they are hard to calculate in. We produce explicit ‘small’ representations of all the maximal subgroups which are not 2-local. The representations we construct are available on the World Wide Web at http://brauer.maths.qmul.ac.uk/Atlas/. 1 The maximal subgroups of the Monster By the work of several authors [13, 14, 17...

Abstract In this paper, we set ? ? ( G stretchy="false">) \eta(G) to be the number of conjugacy classes maximal cyclic subgroups a finite group ????. We compute for all metacyclic ????-groups. show that if ???? is ????-group order <m:msup...