Results 1 to 10 of about 5,724 (262)
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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Some criteria for solvability and supersolvability [PDF]
Journal of Mahani Mathematical Research, 2023 Denote by $ G $ a finite group, by $ {\rm hsn}(G) $ the harmonic mean Sylow number (eliminating the Sylow numbers that are one) in $G$ and by $ {\rm gsn}(G) $ the geometric mean Sylow number (eliminating the Sylow numbers that are one) in $G$.
Zohreh Habibi, Masoomeh Hezarjaribi
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Some remarks on unipotent automorphisms [PDF]
International Journal of Group Theory, 2020 An automorphism $\alpha$ of the group $G$ is said to be $n$-unipotent if $[g,_n\alpha]=1$ for all $g\in G$. In this paper we obtain some results related to nilpotency of groups of $n$-unipotent automorphisms of solvable groups.
Orazio Puglisi, Gunnar Traustason
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Characterizations of Fitting p-Groups whose Proper Subgroups are Solvable [PDF]
Advances in Group Theory and Applications, 2017 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
A.O. Asar
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Corrigendum to: “Characterizations of Fitting p-Groups whose Proper Subgroups are Solvable” [PDF]
Advances in Group Theory and Applications, 2017 The paper entitled "Characterizations of Fitting p-Groups whose Proper Subgroups are Solvable" (Adv. Group Theory Appl. 3 (2017), 31-53) contains a serious error. The proof of Lemma 2.8 relating to p=3 is false.
A.O. Asar
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Corrigendum II to: “Characterization of Fitting p-groups whose proper subgroups are solvable” [PDF]
Advances in Group Theory and Applications, 2018 Unfortunately “Corrigendum to Characterizations of Fitting p-groups whose proper subgroups are solvable” contains an error in the conclusion part of Lemma 2.1 (c).
A.O. Asar
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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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SOLVABILITY OF FREE PRODUCTS, CAYLEY GRAPHS AND COMPLEXES [PDF]
Journal of Algebraic Systems, 2013 In this paper, we verify the solvability of free product of finite cyclic groups with topological methods. We use Cayley graphs and Everitt methods to construct suitable 2-complexes corresponding to the presentations of groups and their commutator ...
Hanieh Mirebrahimi, Fatemeh Ghanei
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A note on finite groups with the indice of some maximal subgroups being primes [PDF]
International Journal of Group Theory, 2017 The Theorem 12 in [A note on $p$-nilpotence and solvability of finite groups, J. Algebra 321 (2009) 1555--1560.] investigated the non-abelian simple groups in which some maximal subgroups have primes indices. In this note we show that this
Cui Zhang
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A Class of Solvable Groups [PDF]
Canadian Journal of Mathematics, 1959 Numerous studies have been made of groups, especially of finite groups, G which have a representation in the form AB, where A and B are subgroups of G. The form of these results is to determine various grouptheoretic properties of G, for example, solvability, from other group-theoretic properties of the subgroups A and B.More recently the structure of ...
Gorenstein, Daniel, Herstein, I. N.
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