Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


On theta pairs for a maximal subgroup

Authors: N. P. Mukherjee and Prabir Bhattacharya
Journal: Proc. Amer. Math. Soc. 109 (1990), 589-596
MSC: Primary 20D10; Secondary 20D25
MathSciNet review: 1015683
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: For a maximal subgroup $ M$ of a finite group $ G$, a $ \Theta $-pair is any pair of subgroups $ (C,D)$ of $ G$ such that (i) $ D \triangleleft G,D \subset C$, (ii) $ \left\langle {M,C} \right\rangle = G,\left\langle {M,D} \right\rangle = M$ and (iii) $ C/D$ has no proper normal subgroup of $ G/D$. A natural partial ordering is defined on the family of $ \Theta $-pairs. We obtain several results on the maximal $ \Theta $-pairs which imply $ G$ to be solvable, supersolvable, and nilpotent.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 20D10, 20D25

Retrieve articles in all journals with MSC: 20D10, 20D25

Additional Information

PII: S 0002-9939(1990)1015683-9
Keywords: Solvable, supersolvable, nilpotent
Article copyright: © Copyright 1990 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia