Geodesic
Equivalent conditions for p-nilpotence
Discussiones Mathematicae. General Algebra and Applications, Tome 20 (2000) no. 1, pp. 129-139

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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.
Keywords: p-nilpotent group, p-constrained group, character of a group, Schmidt group, Thompson-ordering, Sylow p-group 
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Corrádi, Keresztély; Horváth, Erzsébet. Equivalent conditions for p-nilpotence. Discussiones Mathematicae. General Algebra and Applications, Tome 20 (2000) no. 1, pp. 129-139. http://geodesic.mathdoc.fr/item/DMGAA_2000_20_1_a10/