On Fitting groups whose proper subgroups are solvable

Document Type: Research Paper

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Abstract

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.

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