Notes on Infinite Permutation Groups
Bhattacharjee, Meenaxi.
Notes on Infinite Permutation Groups [electronic resource] / by Meenaxi Bhattacharjee, Dugald Macpherson, Rögnvaldur G. Möller, Peter M. Neumann. - XIV, 206 p. online resource. - Lecture Notes in Mathematics, 1698 0075-8434 ; . - Lecture Notes in Mathematics, 1698 .
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.
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.
9783540498131
10.1007/BFb0092550 doi
Group theory.
Group Theory and Generalizations.
QA174-183
512.2
Notes on Infinite Permutation Groups [electronic resource] / by Meenaxi Bhattacharjee, Dugald Macpherson, Rögnvaldur G. Möller, Peter M. Neumann. - XIV, 206 p. online resource. - Lecture Notes in Mathematics, 1698 0075-8434 ; . - Lecture Notes in Mathematics, 1698 .
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.
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.
9783540498131
10.1007/BFb0092550 doi
Group theory.
Group Theory and Generalizations.
QA174-183
512.2