We show that the Graph Isomorphism (GI) problem and the more general problems of String
Isomorphism (SI) andCoset Intersection (CI) can be solved in quasipolynomial (exp ((logn) O …

This book classifies the maximal subgroups of the almost simple finite classical groups in
dimension up to 12; it also describes the maximal subgroups of the almost simple finite …

Permutation Groups form one of the oldest parts of group theory. Through the ubiquity of
group actions and the concrete representations which they afford, both finite and infinite …

A permutation group is said to be quasiprimitive if each of its nontrivial normal subgroups is
transitive. A structure theorem for finite quasiprimitive permutation groups is proved, along …

Following the classification of finite simple groups, one of the major problems in finite group
theory today is the determination of the maximal subgroups of the almost simple groups-that …

Strongly Regular Graphs Page 1 Chapter 9 Strongly Regular Graphs 9.1 Strongly regular
graphs A graph (simple, undirected, and loopless) of order v is called strongly regular with …

Strongly regular graphs lie at the intersection of statistical design, group theory, finite
geometry, information and coding theory, and extremal combinatorics. This monograph …

We present a new approach to analysing finite graphs which admit a vertex intransitive
group of automorphisms $ G $ and are either locally $(G, s) $–arc transitive for $ s\geq 2$ or …

In conversations, correspondence, and even in an attempted but so far still unfinished
survey [12], Kovacs, Saxl and the writer have found that the most effective way of reducing …

An automaton (consisting of a finite set of states with given transitions) is said to be
synchronizing if there is a word in the transitions which sends all states of the automaton to a …