Results 1 to 10 of about 79 (68)
Mathematics, 2020 The structure of the commutator subgroup of Sylow 2-subgroups of an alternating group A 2 k is determined. This work continues the previous investigations of me, where minimal generating sets for Sylow 2-subgroups of alternating groups were ...
Ruslan Skuratovskii
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Characterising Locally Finite Groups Satisfying the Strong Sylow Theorem for the Prime p [PDF]
Advances in Group Theory and Applications, 2022 During his lectures to the 1987 Singapore Group Theory Conference Otto H. Kegel proposed the following question: “If every subgroup S of the locally finite group G contains a finite p-subgroup which is singular in S, does G then satisfy the strong Sylow ...
Felix F. Flemisch
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Finite groups with seminormal or abnormal Sylow subgroups [PDF]
International Journal of Group Theory, 2020 Let $G$ be a finite group in which every Sylow subgroup is seminormal or abnormal. We prove that $G$ has a Sylow tower. We establish that if a group has a maximal subgroup with Sylow subgroups under the same conditions, then this group is ...
Victor Monakhov, Irina Sokhor
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Influence of the number of Sylow subgroups on solvability of finite groups
Comptes Rendus. Mathématique, 2021 Let $G$ be a finite group. We prove that if the number of Sylow $3$-subgroups of $G$ is at most $7$ and the number of Sylow $5$-subgroups of $G$ is at most $1455$, then $G$ is solvable. This is a strong form of a recent conjecture of Robati.
Anabanti, Chimere Stanley +2 more
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On z-Reachable Subgroups of Finite Groups [PDF]
Advances in Group Theory and Applications, 2023 A finite group G is a z-group if every Sylow subgroup of G is cyclic. A subgroup H of a group G is called c-reachable (z-reachable) in G if there is a subgroup chain H = H0 ≤ H1 ≤ ... ≤ Hi ≤ Hi+1 ≤ ... ≤ Hn−1 ≤ Hn = G such that Hi+1 = HiKi, where Ki is a
Victor S. Monakhov, Irina L. Sokhor
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Groups Factorized by Pairwise Permutable Abelian Subgroups of Finite Rank [PDF]
Advances in Group Theory and Applications, 2016 It is proved that a group which is the product of pairwise permutable abelian subgroups of finite Prüfer rank is hyperabelian with finite Prüfer rank; in the periodic case the Sylow subgroups of such a product are described.
Bernhard Amberg, Yaroslav P. Sysak
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Sylow multiplicities in finite groups [PDF]
International Journal of Group Theory, 2018 Let $G$ be a finite group and let $mathcal{P}=P_{1},ldots,P_{m}$ be a sequence of Sylow $p_{i}$-subgroups of $G$, where $p_{1},ldots,p_{m}$ are the distinct prime divisors of $leftvert Grightvert $. The Sylow multiplicity of $gin G$ in $mathcal{
Dan Levy
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Influence of complemented subgroups on the structure of finite groups [PDF]
International Journal of Group Theory, 2021 P. Hall proved that a finite group $G$ is supersoluble with elementary abelian Sylow subgroups if and only if every subgroup of $G$ is complemented in $G$. He called such groups complemented. A. Ballester-Bolinches and X.
Izabela Malinowska
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On the solvability of finite groups and the number of Sylow 2-subgroups [PDF]
European Journal of Mathematics and Applications, 2022 Let $G$ be a finite group. Denoted by $n_2(G)$ the number of Sylow $2$-subgroups of $G$. In this paper, we prove if $G$ is non-solvable and $n_2(G)$ is a power of a prime $p$, then $p$ is a Fermat prime.
Rusong Yang, Kairan Yang, Rulin Shen
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A Simple Classification of Finite Groups of Order p2q2 [PDF]
Mathematics Interdisciplinary Research, 2018 Suppose G is a group of order p2q2 where p>q are prime numbers and suppose P and Q are Sylow p-subgroups and Sylow q-subgroups of G, respectively. In this paper, we show that up to isomorphism, there are four groups of order p2q2 when Q and P are
Aziz Seyyed Hadi +2 more
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