The classification of minimal non-prime-power order groups
type: Item
instance of: scholarly article
title: The classification of minimal non-prime-power order groups
zbMATH Open document ID: 0809.20010
DOI: 10.1007/BF01194842
author: Joseph A. Gallian
author: David Petrie Moulton
published in: Archiv der Mathematik
publication date: 1995-04-03T00:00:00Z
review text: Finite groups all of whose proper subgroups are of prime power order are classified. The results are ``folklore'' and can easily be deduced from results of \textit{L. Rédéi} [Publ. Math. 4, 303-324 (1956; Zbl 0075.240)] on the structure of minimal nonnilpotent groups using standard Hall-Higman reduction [\textit{P. Hall} and \textit{G. Higman}, Proc. Lond. Math. Soc., III. Ser. 6, 1-42 (1956; Zbl 0073.255)]. The methods used in this paper, however, are completely elementary, so that the material can be presented in a graduate course in algebra.
Mathematics Subject Classification ID: 20D10
Mathematics Subject Classification ID: 20D60
Mathematics Subject Classification ID: 20E34
Mathematics Subject Classification ID: 20E07
Mathematics Subject Classification ID: 20D30
Mathematics Subject Classification ID: 20F16
zbMATH DE Number: 572358
zbMATH Keywords: finite groups
zbMATH Keywords: proper subgroups of prime power order
zbMATH Keywords: minimal nonnilpotent groups
reviewed by: Rolf Brandl
MaRDI profile type: Publication
cites work: Q3927385
cites work: Q4692394
cites work: Q4004378
cites work: Finite Groups in Which Every Element Has Prime Power Order
cites work: Endliche Gruppen I
cites work: Q4692427
full work available at URL: https://doi.org/10.1007/bf01194842
OpenAlex ID: W2081720316
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description: scientific article; zbMATH DE number 572358