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A note on p-solvable and solvable finite groups [PDF]
International Journal of Mathematics and Mathematical Sciences, 1994 The notion of normal index is utilized in proving necessary and sufficient conditions for a group G to be respectively, p-solvable and solvable where p is the largest prime divisor of |G|.
R. Khazal, N. P. Mukherjee
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The 3-closure of a solvable permutation group is solvable [PDF]
Journal of Algebra, 2022 Let $m$ be a positive integer and let $Ω$ be a finite set. The $m$-closure of $G\leq\operatorname{Sym}(Ω)$ is the largest permutation group on $Ω$ having the same orbits as $G$ in its induced action on the Cartesian product $Ω^m$. The $1$-closure and $2$-closure of a solvable permutation group need not be solvable.
E.A. O'Brien +3 more
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ON NILALGEBRAS OVER INFINITE FIELD WITH SOLVABLE ASSOCIATED GROUP
Наука и техника, 2006 It is proved that if an associated group A* of a nilalgebra A over an infinite field is solvable of class n then algebra A is solvable of the same class n as the Lie algebra.
M. B. Smirnov
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Minimal irreducible solvable subgroups of the group GL(2, Rp)
Науковий вісник Ужгородського університету. Серія: Математика і інформатика, 2017 All minimal irreducible solvable subgroups of the group GL(2, Rp) (Rp is the ring of integers of the finite ixtension Fp of the fileld rational p-adic numbers Qp for p > 2) are described up to conjugation.
О. А. Кирилюк
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Tarski’s problem for solvable groups [PDF]
Proceedings of the American Mathematical Society, 1986 In this paper, we show that the free solvable groups (as well as the free nilpotent groups) of finite rank have different elementary theories (i.e., they do not satisfy the same first order sentences of group theory). This result is obtained using a result in group theory (probably due to Malcev and following immediately from a theorem of Auslander and
Rogers, Pat +2 more
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