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Mathematics - Algebra | Notes on Infinite Permutation Groups

Notes on Infinite Permutation Groups

Series: Lecture Notes in Mathematics, Vol. 1698

Bhattacharjee, M., Möller, R.G., Macpherson, D., Neumann, P.M.

Jointly published with Hindustan Book Agency, New Dehli, India, 1997

1998, XIV, 206 p.

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The book, based on a course of lectures by the authors at the Indian Institute of Technology, Guwahati, covers aspects of infinite permutation groups theory and some related model-theoretic constructions. There is basic background in both group theory and the necessary model theory, and the following topics are covered: transitivity and primitivity; symmetric groups and general linear groups; wreatch products; automorphism groups of various treelike objects; model-theoretic constructions for building structures with rich automorphism groups, the structure and classification of infinite primitive Jordan groups (surveyed); applications and open problems. With many examples and exercises, the book is intended primarily for a beginning graduate student in group theory.

Content Level » Research

Keywords » Group theory - Jordan group - automorphism group - combinatorics - homogeneous structures - model Theory - permutation group

Related subjects » Algebra

Table of contents 

Some group theory.- Groups acting on sets.- Transitivity.- Primitivity.- Suborbits and orbitals.- More about symmetric groups.- Linear groups.- Wreath products.- Rational numbers.- Jordan groups.- Examples of Jordan groups.- Relations related to betweenness.- Classification theorems.- Homogeneous structures.- The Hrushovski construction.- Applications and open questions.

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Distribution rights for India: Hindustan Book Agency, New Delhi, India

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