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Weakly totally permutable products and Fitting classes | ||
| International Journal of Group Theory | ||
| مقاله 17، دوره 10، شماره 1، خرداد 2021، صفحه 31-38 اصل مقاله (187.16 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2019.115685.1535 | ||
| نویسنده | ||
| Sesuai Yash Madanha* | ||
| Department of Mathematics and Applied Mathematics, University of Pretoria, Private bag X20, Hatfield, 0028, Pretoria, South Africa | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| weakly totally permutable products؛ mutually permutable products؛ Fitting classes | ||
| مراجع | ||
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[1] A. Ballester-Bolinches, R. Esteban-Romero and M. Asaad, Products of Finite Groups, Walter De Gruyter, BerlinNew York, 2010.
[2] A. Ballester-Bolinches, M. C. Pedraza-Aguilera and M. D. P´erez-Ramos, Finite groups which are products of pairwise totally permutable subgroups, Proc. of the Edin. Math. Soc., 41 (1998) 567–572. [3] J. C. Beidleman and H. Heineken, Mutually permutable subgroups and group classes, Arch. Math., 85 (2005) 18–30.
[4] J. Bochtler and P. Hauck, Mutually permutable subgroups and Fitting classes, Arch. Math., 88 (2007) 385–388.
[5] K. Doerk and T. O. Hawkes, Finite Soluble Groups, Walter De Gruyter, Berlin-New York, (1992).
[6] P. Hauck, A. Mart´ınez-Pastor and M. D. P´erez-Ramos, Fitting classes and products of totally permutable groups, J. Algebra, 252 (2002) 114–126. [7] S. Y. Madanha, On a generalisation of totally permutable products of finite groups, J. Algebra, 358 (2012) 1–7. | ||
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