Subgroup Growth
by Dan Segal /
2003 / English / PDF
3.5 MB Download
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 the last two
decades this topic has developed into one of the most active areas
of research in infinite group theory; this book is a systematic and
comprehensive account of the substantial theory which has emerged.
As well as determining the range of possible 'growth types', for
finitely generated groups in general and for groups in particular
classes such as linear groups, a main focus of the book is on the
tight connection between the subgroup growth of a group and its
algebraic structure. A wide range of mathematical disciplines play
a significant role in this work: as well as various aspects of
infinite group theory, these include finite simple groups and
permutation groups, profinite groups, arithmetic groups and Strong
Approximation, algebraic and analytic number theory, probability,
and p-adic model theory. Relevant aspects of such topics are
explained in self-contained 'windows'.
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 the last two
decades this topic has developed into one of the most active areas
of research in infinite group theory; this book is a systematic and
comprehensive account of the substantial theory which has emerged.
As well as determining the range of possible 'growth types', for
finitely generated groups in general and for groups in particular
classes such as linear groups, a main focus of the book is on the
tight connection between the subgroup growth of a group and its
algebraic structure. A wide range of mathematical disciplines play
a significant role in this work: as well as various aspects of
infinite group theory, these include finite simple groups and
permutation groups, profinite groups, arithmetic groups and Strong
Approximation, algebraic and analytic number theory, probability,
and p-adic model theory. Relevant aspects of such topics are
explained in self-contained 'windows'.
