Mathematics and Statistics Vol. 2(7), pp. 238 - 239
DOI: 10.13189/ms.2014.020703
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Non-nilpotent Subgroups in Locally Graded Groups

N. Azimi , M. Amirabadi ^*
Department of Mathematics, Hamedan branch, Islamic azad University, Hamedan, Iran

ABSTRACT

A non-nilpotent finite group whose proper subgroups are all nilpotent (or a finite group without non-nilpotent proper subgroups) is well-known (called Schmidt group). O.Yu. Schmidt (1924) studied such groups and proved that such groups are solvable. More recently Zarrin generalized Schmidt's Theorem and proved that every finite group with less than 22 non-nilpotent subgroups is solvable. In this paper, we show that every locally graded group with less than 22 non-nilpotent subgroups is solvable.

KEYWORDS
Schmidt Group, Locally Graded Group, Solvable Group

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] N. Azimi , M. Amirabadi , "Non-nilpotent Subgroups in Locally Graded Groups," Mathematics and Statistics, Vol. 2, No. 7, pp. 238 - 239, 2014. DOI: 10.13189/ms.2014.020703.

(b). APA Format:
N. Azimi , M. Amirabadi (2014). Non-nilpotent Subgroups in Locally Graded Groups. Mathematics and Statistics, 2(7), 238 - 239. DOI: 10.13189/ms.2014.020703.