Finite Groups Having Exactly 34 Elements of Maximal Order

Maximal subsets of pairwise non-commuting elements of some finite p-groups

Let G be a group. A subset X of G is a set of pairwise noncommuting elements if xy ̸= yx for any two distinct elements x and y in X. If |X| ≥ |Y | for any other set of pairwise non-commuting elements Y in G, then X is said to be a maximal subset of pairwise non-commuting elements. In this paper we determine the cardinality of a maximal subset of pairwise non-commuting elements in any non-abelian...

Maximal Length Elements of Excess Zero in Finite Coxeter Groups

Elements of finite order in automorphism groups of homogeneous structures

We study properties of the automorphism groups of Fräıssé limits of classes with certain strong amalgamation properties, including classes with the free amalgamation property and classes of metric spaces. We discuss conditions on a Fräıssé class K that imply that the automorphism group GK of its limit admits generic elements of order n for all n and show that, for many such K, any element of GK...

maximal subsets of pairwise non-commuting elements of some finite p-groups

let g be a group. a subset x of g is a set of pairwise noncommuting elements if xy ̸= yx for any two distinct elements x and y in x. if |x| ≥ |y | for any other set of pairwise non-commuting elements y in g, then x is said to be a maximal subset of pairwise non-commuting elements. in this paper we determine the cardinality of a maximal subset of pairwise non-commuting elements in any non-abelian...

Maximal Subgroups of Finite Groups

What ingredients are necessary to describe all maximal subgroups of the general finite group G? This paper is concerned with providing such an analysis. A good first reduction is to take into account the first isomorphism theorem, which tells us that the maximal subgroups containing a given normal subgroup N of G correspond, under the natural projection, to the maximal subgroups of the quotient...