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Symmetric Inverse Semigroups; Mathematical Surveys & Monographs; by Stephen Leon Lipscomb is a nonfiction available to read on EtoBox.

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<p>With over 60 figures, tables, and diagrams, this text is both an intuitive introduction to and a rigorous study of finite symmetric inverse semigroups. The model, denoted $C_n$, consists of all charts (one-one partial transformations) of the set ${1,\dots,n}$ under the usual composition of mappings. It has the symmetric groups $S_n$ as a subgroup, and many classical features of $S_n$ are extended to $C_n$. It turns out that these semigroups enjoy many of the classical features of finite symmetric groups. For example, cycle notation, conjugacy, commutativity, parity of permutations, alternating subgroups, Klein 4-group, Ruffini's result on cyclic groups, Moore's presentations of the symmetric and alternating groups, and the centralizer theory of symmetric groups are extended to more general counterparts in $C_n$. Lipscomb classifies normal subsemigroups and also illustrates and applies an Eilenberg-style wreath product. The basic $C_n$ theory is further extended to partial transformation semigroups, and the Reconstruction Conjecture of graph theory is recast as a Rees' ideal-extension conjecture. This books presents much of the material on the theory of finite symmetric inverse s

Who reads Symmetric Inverse Semigroups; Mathematical Surveys & Monographs;?

Author

Stephen Leon Lipscomb

Publisher

American Mathematical Society(ri)

Published

1996

Language

EN

ISBN

9783919891792

Category

nonfiction

Subjects

Political Science, Science, Business