We show that a locally graded group with a finite number m of non-(nilpotent of class at most n) subgroups is (soluble of class at most [log₂n] + m + 3)-by-(finite of order ≤ m!). We also show that the derived length of a soluble group with a finite number m of non-(nilpotent of class at most n) subgroups is at most [log₂ n] + m + 1.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm138-1-9,
author = {Mohammad Zarrin},
title = {Non-nilpotent subgroups of locally graded groups},
journal = {Colloquium Mathematicae},
volume = {139},
year = {2015},
pages = {145-148},
zbl = {1312.20035},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm138-1-9}
}
Mohammad Zarrin. Non-nilpotent subgroups of locally graded groups. Colloquium Mathematicae, Tome 139 (2015) pp. 145-148. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm138-1-9/