Discussiones
Mathematicae General Algebra and Applications 20(1) (2000) 129-139
DOI: https://doi.org/10.7151/dmgaa.1011
EQUIVALENT CONDITIONS FOR P-NILPOTENCE
Keresztély Corrádi and Erzsébet Horváth
Eötvös Loránd University, Department of Computer
Techn.
H-1088 Budapest, Múzeum krt. 6-8
Technical University of Budapest, Department of Algebra
H-1521 Budapest, Muegyetem rkp. 3-9
e-mail: he@math.bme.hu
Abstract
In the first part of this paper we prove without using the transfer or characters the equivalence of some conditions, each of which would imply p-nilpotence of a finite group G. The implication of p-nilpotence also can be deduced without the transfer or characters if the group is p-constrained. For p-constrained groups we also prove an equivalent condition so that Oq′(G)P should be p-nilpotent. We show an example that this result is not true for some non-p-constrained groups.
In the second part of the paper we prove a generalization of a theorem of Itô with the help of the knowledge of the irreducible characters of the minimal non-nilpotent groups.
Keywords: p-nilpotent group, p-constrained group, character of a group, Schmidt group, Thompson-ordering, Sylow p-group.
1991 Mathematics Subject Classification: 20D15 and 20C15.
References
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Received 25 January 1999
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