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On Fitting groups whose proper subgroups are solvable | ||
| International Journal of Group Theory | ||
| مقاله 2، دوره 5، شماره 2، شهریور 2016، صفحه 7-24 اصل مقاله (252.67 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2016.6250 | ||
| نویسنده | ||
| Ali Osman Asar* | ||
| No affiliation | ||
| چکیده | ||
| This work is a continuation of [A. O. Asar, On infinitely generated groups whose proper subgroups are solvable, J. Algebra, 399 (2014) 870-886.], where it was shown that a perfect infinitely generated group whose proper subgroups are solvable and in whose homomorphic images normal closures of finitely generated subgroups are residually nilpotent is a Fitting $p$-group for a prime $p$. Thus this work is a study of a Fitting $p$-group whose proper subgroups are solvable. New characterizations and some sufficient conditions for the solvability of such a group are obtained. | ||
| کلیدواژهها | ||
| Fitting group؛ normalizer؛ Engel condition | ||
| مراجع | ||
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A. O. Asar (2011) Totally imprimitive permutation groups with the cyclic-block property J. Group Theory 14, 127-141
A. O. Asar (2014) On infinitely generated groups whose proper subgroups are solvable J. Algebra 399, 870-886
G. Endimioni and G. Traustason (2001) On torsion-by-nilpotent groups J. Algebra 241, 669-676
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D. J. S. Robinson (1980) A Course in the Theory of Groups Springer-Verlag, New York, Heidelberg, Berlin
P. Shumyatsky (2003) On extensions of groups of finite exponent Glasg. Math. J. 45, 535-538
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