Characterizations of Fitting p-Groups whose Proper Subgroups are Solvable

This work continues the study of infinitely generated groups whose proper subgroups are solvable and in whose homomorphic images normal closures of finitely generated subgroups are residually nilpotent. In [4], it has been shown that such a group, if not solvable, is a perfect Fitting p-group for a prime p with additional restrictions. Therefore this work is a study of Fitting p-groups whose proper subgroups are solvable. Here a condition is given for the imperfectness of a Fitting $p$-group satisfying the normalizer condition, where $p\neq 2$. Hence it follows that if every proper subgroup of the group in question is solvable, then the group itself is solvable. Furthermore some conditions are given for a perfect Fitting $p$-group whose proper subgroups are solvable in order for the subgroup generated by normal subgroups of a given derived length to be proper, where $p\neq 2$