Equivalent conditions for p-nilpotence

Keresztély Corrádi; Erzsébet Horváth

Discussiones Mathematicae - General Algebra and Applications (2000)

  • Volume: 20, Issue: 1, page 129-139
  • ISSN: 1509-9415

Abstract

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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 O q ' ( 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.

How to cite

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Keresztély Corrádi, and Erzsébet Horváth. "Equivalent conditions for p-nilpotence." Discussiones Mathematicae - General Algebra and Applications 20.1 (2000): 129-139. <http://eudml.org/doc/287702>.

@article{KeresztélyCorrádi2000,
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 $O^\{q^\{\prime \}\}(G)P$ 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.},
author = {Keresztély Corrádi, Erzsébet Horváth},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {p-nilpotent group; p-constrained group; character of a group; Schmidt group; Thompson-ordering; Sylow p-group; -nilpotency; transfer; characters; -constrained groups},
language = {eng},
number = {1},
pages = {129-139},
title = {Equivalent conditions for p-nilpotence},
url = {http://eudml.org/doc/287702},
volume = {20},
year = {2000},
}

TY - JOUR
AU - Keresztély Corrádi
AU - Erzsébet Horváth
TI - Equivalent conditions for p-nilpotence
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2000
VL - 20
IS - 1
SP - 129
EP - 139
AB - 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 $O^{q^{\prime }}(G)P$ 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.
LA - eng
KW - p-nilpotent group; p-constrained group; character of a group; Schmidt group; Thompson-ordering; Sylow p-group; -nilpotency; transfer; characters; -constrained groups
UR - http://eudml.org/doc/287702
ER -

References

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  1. [1] J.L. Alperin, Centralizers of abelian normal subgroups of p-groups, J. Algebra 1 (1964), 110-113. Zbl0119.02901
  2. [2] K. Corrádi, On certain properties of centralizers hereditary to the factor group, Publ. Math. (Debrecen) 37 (1990), 203-206. Zbl0722.20012
  3. [3] K. Corrádi and E. Horváth, Steps towards an elementary proof of Frobenius' theorem, Comm. Algebra 24 (1996), 2285-2292. Zbl0856.20017
  4. [4] K. Corrádi and E. Horváth, Normal π-complement theorems, Arch. Math. (Basel) 71 (1998), 262-269. Zbl0921.20023
  5. [5] D. Gorenstein, 'Finite groups', Chelsea Publ. Comp., New York 1980. Zbl0463.20012
  6. [6] B. Huppert, 'Endliche Gruppen', Springer-Verlag, Berlin 1967. Zbl0189.31601
  7. [7] I.M. Isaacs, 'Character theory of finite groups', Dover Publ., Inc., New York 1994. Zbl0849.20004
  8. [8] N. Itô, On a theorem of H.F. Blichfeldt, Nagoya Math. J. 5 (1953), 75-77. 

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