John N. Bray

A CHARACTERIZATION OF FINITE SOLUBLE GROUPS BY LAWS IN TWO VARIABLES

Define a sequence (sn) of two-variable words in variables x, y as follows: s0(x, y) = x, sn+1(x, y) = [sn(x, y)−y, sn(x, y)] for n > 0. It is shown that a finite group G is soluble if and only if sn is a law of G for all but finitely many values of n.

A systematic approach to symmetric presentations. I. Involutory generators

In this paper we conduct a systematic, computerized search for groups generated by small, but highly symmetric, sets of involutions. Many classical groups are readily obtained in this way, as are a number of sporadic simple groups. The techniques of symmetric generation developed elsewhere are described afresh, and the results are presented in a convenient tabular form.

ON THE ORDERS OF AUTOMORPHISM GROUPS OF FINITE GROUPS

In the Kourovka notebook , Deaconescu asks whether

Short presentations for alternating and symmetric groups

\gpord{\Aut G}\ge \phi(\gpord{G})

Cayley type graphs and cubic graphs of large girth

for all finite groups

Monomial modular representations and symmetric generation of the Harada–Norton group

G

Examples of 3-dimensional 1-cohomology for absolutely irreducible modules of finite simple groups

, where

Decoding the Mathieu group M 12

\phi

Symmetric presentations for the Fischer groups I: the classical groups Sp6(2), Sp8(2), and 3·O7(3)

denotes the Euler totient function, and whether

A systematic approach to symmetric presentations II: Generators of order 3

G