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Polynomial Ideals and Classes of Finite Groups

✍ Scribed by Serge Bouc

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 150 KB
Volume: 229
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.2000.8303

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✦ Synopsis

The object of this note is to discuss the properties of some polynomials on a . countable set of indeterminates attached to any finite group which generalize the Ž Eulerian functions of a group defined by P. Hall 1936, Quart. J. Math. 7, . 134᎐151 . In particular, I will define some classes of finite groups associated to prime ideals of the polynomial ring, and I will show that each finite group has a unique largest quotient in such a class of groups.

This work is a generalization of the notion of the b-group introduced in an Ž . earlier paper Bouc, 1996, J. Algebra 183, 664᎐736 through a systematic use of the polynomial formalism of Section 7.2.5 there. For the reader's convenience, however, this paper is self-contained and the proofs of the results already stated are included.

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