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The order of groups satisfying a converse to Lagrange's theorem

Part of: Special aspects of infinite or finite groups

Published online by Cambridge University Press:  26 February 2010

Naihuan Jing
Naihuan Jing
Affiliation:
Department of Mathematics, North Carolina State University, Raleigh, NC 27695-8205, U.S.A. E-mail: jing@math.ncsu.edu
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Abstract

One of the converse statements to Lagrange's theorem is that, for each subgroup H of G and any prime factor p of |G: H|, there exists a subgroup K such that H≤K≤G with |K: H | = p. This paper treats integers n such that all groups of order n have this property.

MSC classification

Secondary: 20F16: Solvable groups, supersolvable groups
Type
Research Article
Information
Mathematika , Volume 47 , Issue 1-2 , December 2000 , pp. 197 - 204
Copyright
Copyright © University College London 2000

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