Results 1 to 10 of about 1,123 (138)
Some results on π-solvable and supersolvable groups [PDF]
International Journal of Mathematics and Mathematical Sciences, 1994 For a finite group G, ϕp(G), Sp(G), L(G) and S𝒫(G) are generalizations of the Frattini subgroup of G. We obtain some results on π-solvable, p-solvable and supersolvable groups with the help of the structures of these subgroups.
T. K. Dutta, A. Bhattacharyya
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ON THE SUPERSOLVABILITY OF BICYCLIC GROUPS. [PDF]
Proc Natl Acad Sci U S A, 1961 Douglas J.
europepmc +7 more sources
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 the commuting probability and supersolvability of finite groups [PDF]
, 2013 For a finite group $G$, let $d(G)$ denote the probability that a randomly chosen pair of elements of $G$ commute. We prove that if $d(G)>1/s$ for some integer $s>1$ and $G$ splits over an abelian normal nontrivial subgroup $N$, then $G$ has a nontrivial ...
Lescot, Paul +2 more
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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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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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Gallery Posets of Supersolvable Arrangements [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 We introduce a poset structure on the reduced galleries in a supersolvable arrangement of hyperplanes. In particular, for Coxeter groups of type A or B, we construct a poset of reduced words for the longest element whose Hasse diagram is the graph of ...
Thomas McConville
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