-groups.
Characterization of finite groups by their commuting graph.
Characterization of -solvable groups.
Characterization of by its non-commuting graph.
Characterization of the alternating groups by their order and one conjugacy class length
Let be a finite group, and let be the set of conjugacy class sizes of . By Thompson’s conjecture, if is a finite non-abelian simple group, is a finite group with a trivial center, and , then and are isomorphic. Recently, Chen et al. contributed interestingly to Thompson’s conjecture under a weak condition. They only used the group order and one or two special conjugacy class sizes of simple groups and characterized successfully sporadic simple groups (see Li’s PhD dissertation). In...
Commutative subloop-free loops
We describe, in a constructive way, a family of commutative loops of odd order, , which have no nontrivial subloops and whose multiplication group is isomorphic to the alternating group .
Construction of 2-local finite groups of a type studied by Solomon and Benson.
Correction to the paper “Generators of an orthogonal group over a finite field”
Coset enumeration of groups generated by symmetric sets of involutions.
Crossed product of cyclic 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.