Permutation groups are one of the oldest topics in algebra. Their study has recently been
revolutionized by new developments, particularly the Classification of Finite Simple Groups …

Permutation group algorithms are one of the workhorses of symbolic algebra systems
computing with groups. They played an indispensable role in the proof of many deep results …

Award-winning monograph of the Ferran Sunyer i Balaguer Prize 2001. Subgroup growth
studies the distribution of subgroups of finite index in a group as a function of the index. In …

In this paper we discuss the basic problems of algorithmic algebraic number theory. The
emphasis is on aspects that are of interest from a purely mathematical point of view, and …

The Absolute Centre of a Group Page 1 yt i NAI, ) A ; , 169, 929-935 (1994) The Absolute
Centre of a Group PETER HEGARTY Department of Mathematics, Unitersity College, Cork …

It is well known that every finite simple group can be generated by two elements and this
leads to a wide range of problems that have been the focus of intensive research in recent …

Let f (n) denote the number of (isomorphism classes of) groups of order n. Let n= HW p9ig
be the prime factorization of n and let A= A (n)= Ek and, u= ii (n)= maxkL1 gi. The function f …

Finite Groups Have Many Conjugacy Classes Page 1 FINITE GROUPS HAVE MANY
CONJUGACY CLASSES L. PYBER ABSTRACT We prove that every group of order n contains …

We present some questions that we feel are important and interesting for the theory of finite
p-groups, and survey known results regarding these questions. Mike, the other year you …

We obtain a surprisingly explicit formula for the number of random elements needed to
generate a finite d-generator group with high probability. As a corollary we prove that if G is …