A generalization of Schmidt’s Theorem on groups with all subgroups nilpotent

Zarrin, Mohammad

doi:10.1007/s00013-012-0411-1

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Introduction4

Now We Prove Theorem B1

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Cited by 9 publications

(16 citation statements)

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“…Finally, as every S m n -group is a S r -group, for some r ≤ m, and by the main result in [9], we can see that every S m n -group with m ≤ 21 is soluble. Hence the following question arises naturally: Question 2.1.…”

Section: Now We Prove Theorem Bmentioning

confidence: 65%

Non-nilpotent subgroups of locally graded groups

Zarrin

2015

Colloq. Math.

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Section: Now We Prove Theorem Bmentioning

confidence: 65%

Non-nilpotent subgroups of locally graded groups

Zarrin

2015

Colloq. Math.

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“…There have been several results that investigate, in a quantitative way, the influences of properties of subgroups on the structure of the whole group. For example in [2] it was shown that an insoluble group has exactly 22 non-nilpotent subgroups if and only if it is isomorphic to A 5 or SL (2,5) and that confirmed a conjecture of Zarrin [17].…”

Section: Introduction and Notationmentioning

confidence: 70%

Finite groups with few normalizers or involutions

Malinowska

2019

Arch. Math.

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The groups having exactly one normalizer are Dedekind groups. All finite groups with exactly two normalizers were classified by Pérez-Ramos in 1988. In this paper we prove that every finite group with at most 26 normalizers of {2, 3, 5}-subgroups is soluble and we also show that every finite group with at most 21 normalizers of cyclic {2, 3, 5}subgroups is soluble. These confirm Conjecture 3.7 of Zarrin (Bull Aust Math Soc 86:416-423, 2012).

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“…Therefore one can see that every finite n-A -critical groups with n ≤ 21 is solvable Russo [14] studied 2-N -critical groups, where N is the class of nilpotent groups, in infinite case and obtained some results in finite case. Also by the main result in [18], one can see that every finite n-N -critical groups with n ≤ 21 is solvable.…”

Section: Introductionmentioning

confidence: 90%