Results 11 to 20 of about 1,123 (134)
International Journal of Mathematics and Mathematical Sciences, 1997 Let G be a finite group and H be an operator group of G. In this short note, we show a relationship between subnormal subgroup chains and H-invariant subgroup chains.
Yanming Wang
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On Supersolvable Groups and a Theorem of Huppert [PDF]
Canadian Mathematical Bulletin, 1990 AbstractWe obtain the following generalization of a well known result of Huppert. If p is the largest primer divisor of the order of a finite group G and q is any prime distinct from p, then G is supersolvable if and only if every maximal subgroup whose index is relatively prime to either p or q, has prime index.
N. P. Mukherjee, Prabir Bhattacharya
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On some sufficient conditions of supersolvability of finite groups
Publicationes Mathematicae Debrecen, 2004 A subgroup \(H\) of a group \(G\) is called \(c\)-supplemented if there exists a subgroup \(K\) of \(G\) such that \(G=HK\) and \(H\cap K\leq H_G\). In this paper, among other results, the authors prove that if a finite group \(G\) contains a quaternion-free normal subgroup \(N\) such that \(G/N\) is supersoluble and every subgroup of prime order of ...
Yanming Wang, Yangming Li
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A Generalization of Hall-Complementation in Finite Supersolvable Groups [PDF]
Transactions of the American Mathematical Society, 1969 g*: For each normal subgroup N$ 'P(G), each reduced product of G over N is a semidirect product. (G = NB is a reduced product over a normal subgroup N by a subgroup B iff B does not contain a proper subgroup B* such that G = NB*.) F. Gross [5] has shown that for a finite solvable group G having 4!(G) = 1, splitting over each normal subgroup is ...
Homer Bechtell
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Characterization of finite groups with a unique non-nilpotent proper subgroup [PDF]
International Journal of Group Theory, 2021 We characterize finite non-nilpotent groups $G$ with a unique non-nilpotent proper subgroup. We show that $|G|$ has at most three prime divisors. When $G$ is supersolvable we find the presentation of $G$ and when $G$ is non-supersolvable we show ...
Bijan Taeri, Fatemeh Tayanloo-Beyg
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, 2012 One important problem in Q-gruops theory is to classify particular dasses of Q-groups.
Ion Armeanu
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The structure of groups with cyclic commutator subgroups indecomposable to a subdirect product of groups [PDF]
Известия Саратовского университета. Новая серия: Математика. Механика. Информатика, 2021 The article studies finite groups indecomposable to subdirect product of groups (subdirectly irreducible groups), commutator subgroups of which are cyclic subgroups.
Kozlov, Vladimir Anatolievich +1 more
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A note on $1$-factorizability of quartic supersolvable Cayley graphs [PDF]
Transactions on Combinatorics, 2018 Alspach et al. conjectured that every quartic Cayley graph on an even solvable group is $1$-factorizable. In this paper, we verify this conjecture for quartic Cayley graphs on supersolvable groups of even order.
Milad Ahanjideh, Ali Iranmanesh
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Maximal Subgroup Containment in Direct Products [PDF]
Advances in Group Theory and Applications, 2016 Using the main theorem from [1] that characterizes containment of subgroups in a direct product, we provide a characterization of maximal subgroups contained in a direct product.
Ben Brewster, Dandrielle Lewis
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On non-normal cyclic subgroups of prime order or order 4 of finite groups
Open Mathematics, 2021 In this paper, we call a finite group GG an NLMNLM-group (NCMNCM-group, respectively) if every non-normal cyclic subgroup of prime order or order 4 (prime power order, respectively) in GG is contained in a non-normal maximal subgroup of GG.
Guo Pengfei, Han Zhangjia
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