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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 co-maximal subgroup graph of $Z_n$ [PDF]
International Journal of Group Theory, 2022 The co-maximal subgroup graph $\Gamma(G)$ of a group $G$ is a graph whose vertices are non-trivial proper subgroups of $G$ and two vertices $H$ and $K$ are adjacent if $HK = G$.
Manideepa Saha +2 more
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On a Maximal Subgroup 2^6:(3^. S6) of M24 [PDF]
Mathematics Interdisciplinary Research, 2022 The Mathieu group M24 has a maximal subgroup of the form G ̅=N:G, where N=26 and G=3. S6 ≅ 3. PGL2 (9). Using Atlas, we can see that M24 has only one maximal subgroup of type 26:(3. S6). The group is a split extension of an elementary abelian group, N=26
Dennis Chikopela, Thekiso Seretlo
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On a maximal subgroup of the Symplectic group Sp(4,4) [PDF]
AUT Journal of Mathematics and Computing, 2023 This paper is dealing with a split extension group of the form 26 :(3× A5), which is the largest maximal subgroup of the Symplectic group Sp(4, 4). We refer to this extension by G.
Ayoub Basheer
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Generation of Finite Groups and Maximal Subgroup Growth [PDF]
Advances in Group Theory and Applications, 2020 Let G be a finite group and, for n 2 N, denote by m_n(G) the number of maximal subgroups of G with index n. Let M(G) = sup_{n>2} log m_n(G)/log n and let E_1(G) be the expected number of elements of G which have to be drawn at random, with ...
Andrea Lucchini, Mariapia Moscatiello
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Algebraic subgroups of the plane Cremona group over a perfect field [PDF]
Épijournal de Géométrie Algébrique, 2021 We show that any infinite algebraic subgroup of the plane Cremona group over a perfect field is contained in a maximal algebraic subgroup of the plane Cremona group.
Julia Schneider, Susanna Zimmermann
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Locally Maximal Subgroups and the Normalizer Condition in p-Groups [PDF]
Advances in Group Theory and Applications, 2023 This work is a continuation of the investigation of a locally nilpotent p-group satisfying the normalizer condition by imposing certain conditions on locally maximal subgroups, where p ≠ 2.
A.O. Asar
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The reduction theorem for relatively maximal subgroups
Bulletin of Mathematical Sciences, 2022 Let [Formula: see text] be a class of finite groups closed under taking subgroups, homomorphic images and extensions. It is known that if [Formula: see text] is a normal subgroup of a finite group [Formula: see text] then the image of an [Formula: see ...
Wenbin Guo +2 more
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Designs from maximal subgroups and conjugacy classes of $\mathrm{PSL}(2,q)$, $q$ odd [PDF]
AUT Journal of Mathematics and Computing, 2023 In this paper, using a method of construction of $1$-designs which are not necessarily symmetric, introduced by Key and Moori, we determine a number of $1$-designs with interesting parameters from the maximal subgroups and the conjugacy classes of ...
Xavier Mbaale +2 more
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Bounds on the Number of Maximal Subgroups of Finite Groups: Applications
Mathematics, 2022 The determination of bounds for the number of maximal subgroups of a given index in a finite group is relevant to estimate the number of random elements needed to generate a group with a given probability.
Adolfo Ballester-Bolinches +2 more
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