Symmetric generation of groups : with applications to many of the sporadic finite simple groups / Robert T. Curtis.

By:

Curtis, Robert, 1946- [author.]

Contributor(s):

Cambridge eBooks

Series: Encyclopedia of mathematics and its applications ; v. 111.Publisher: Cambridge : Cambridge University Press, 2007Description: 1 online resource (xiv, 317 pages) : digital, PDF file(s)Content type:

text

Media type:

computer

Carrier type:

online resource

ISBN:

9780511661792 (ebook)

Subject(s):

Genre/Form:

Electronic books.

Additional physical formats: Print version: : No titleDDC classification:

512.2 22

LOC classification:

QA177 .C87 2007

Online resources:

Click here to access online

Contents:

Motivation -- Involutory symmetric generators -- Non-involutory symmetric generators.

Summary: Some of the most beautiful mathematical objects found in the last forty years are the sporadic simple groups. But gaining familiarity with these groups presents problems for two reasons. Firstly, they were discovered in many different ways, so to understand their constructions in depth one needs to study lots of different techniques. Secondly, since each of them is in a sense recording some exceptional symmetry in spaces of certain dimensions, they are by their nature highly complicated objects with a rich underlying combinatorial structure. Motivated by initial results which showed that the Mathieu groups can be generated by highly symmetrical sets of elements, which themselves have a natural geometric definition, the author develops from scratch the notion of symmetric generation. He exploits this technique by using it to define and construct many of the sporadic simple groups including all the Janko groups and the Higman-Sims group. For researchers and postgraduates.

Item type:

eBooks

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Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Motivation -- Involutory symmetric generators -- Non-involutory symmetric generators.

Some of the most beautiful mathematical objects found in the last forty years are the sporadic simple groups. But gaining familiarity with these groups presents problems for two reasons. Firstly, they were discovered in many different ways, so to understand their constructions in depth one needs to study lots of different techniques. Secondly, since each of them is in a sense recording some exceptional symmetry in spaces of certain dimensions, they are by their nature highly complicated objects with a rich underlying combinatorial structure. Motivated by initial results which showed that the Mathieu groups can be generated by highly symmetrical sets of elements, which themselves have a natural geometric definition, the author develops from scratch the notion of symmetric generation. He exploits this technique by using it to define and construct many of the sporadic simple groups including all the Janko groups and the Higman-Sims group. For researchers and postgraduates.