Weakly totally permutable products and Fitting classes
Publish place: International Journal of Group Theory، Vol: 10، Issue: 1
Publish Year: 1400
نوع سند: مقاله ژورنالی
زبان: English
View: 127
This Paper With 8 Page And PDF Format Ready To Download
- Certificate
- من نویسنده این مقاله هستم
استخراج به نرم افزارهای پژوهشی:
شناسه ملی سند علمی:
JR_THEGR-10-1_003
تاریخ نمایه سازی: 14 اردیبهشت 1400
Abstract:
It is known that if $ G=AB $ is a product of its totally permutable subgroups $ A $ and $ B $, then $ G\in \mathfrak{F} $ if and only if $ A\in \mathfrak{F} $ and $ B\in \mathfrak{F} $ when $ \mathfrak{F} $ is a Fischer class containing the class $ \mathfrak{U} $ of supersoluble groups. We show that this holds when $ G=AB $ is a weakly totally permutable product for a particular Fischer class, $ \mathfrak{F}\diamond \mathfrak{N} $, where $ \mathfrak{F} $ is a Fitting class containing the class $ \mathfrak{U} $ and $ \mathfrak{N} $ a class of nilpotent groups. We also extend some results concerning the $ \mathfrak{U} $-hypercentre of a totally permutable product to a weakly totally permutable product.
Keywords:
Authors
Sesuai Madanha
Department of Mathematics and Applied Mathematics, University of Pretoria, Private bag X۲۰, Hatfield, ۰۰۲۸, Pretoria, South Africa