Results 1 to 10 of about 47 (34)
A note on groups with a finite number of pairwise permutable seminormal subgroups [PDF]
International Journal of Group Theory, 2022 Summary: A subgroup \(A\) of a group \(G\) is called \textit{seminormal} in \(G\), if there exists a subgroup \(B\) such that \(G = AB\) and \(AX\) is a subgroup of \(G\) for every subgroup \(X\) of \(B\). The group \(G = G_1 G_2\cdots G_n\) with pairwise permutable subgroups \(G_1, \dots, G_n\) such that \(G_i\) and \(G_j\) are seminormal in \(G_iG_j\)
Alexander Trofimuk
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Finite groups with seminormal or abnormal Sylow subgroups [PDF]
International Journal of Group Theory, 2019 Summary: 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 soluble.
Monakhov, Victor Stepanovich +1 more
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Seminormal, Non-Normal Maximal Subgroups and Soluble PST-Groups [PDF]
Advances in Group Theory and Applications, 2016 All groups in this paper are finite. Let G be a group. Maximal subgroups of G are used to establish several new characterisations of soluble PST-groups.
J.C. Beidleman
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On seminormal subgroups of finite groups
Rocky Mountain Journal of Mathematics, 2017 All groups considered in this paper are finite. A subgroup~$H$ of a group~$G$ is said to \textit {seminormal} in $G$ if $H$ is normalized by all subgroups~$K$ of~$G$ such that $\gcd (\lvert H\rvert , \lvert K\rvert )=1$. We call a group $G$ an MSN-\textit {group} if the maximal subgroups of all the Sylow subgroups of~$G$ are seminormal in~$G$.
A Ballester-Bolinches, J C Beidleman
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Journal of Algebra, 1994 A subgroup \(H\) of a finite group \(G\) is defined to be seminormal in \(G\) if it permutes with every subgroup of \(G\) whose order is relatively prime to the order of \(H\). Clearly a subgroup of prime index in \(G\) is seminormal in \(G\), and the author shows this is necessary when \(G\) is simple and \(H\) is proper and nontrivial.
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The Existence of pblocks of Defect 0 in a Finite Groups with Some Subgroups Being Seminormal
Journal of Harbin University of Science and Technology, 2020 By studying homogeneous polynomials related to groups, the complex index of finite groups is defined.The theory of complex index and its complex representation has been developed and perfected quickly So people began to consider the representation of ...
WANG Hong, QIAN Fangsheng
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International Journal of Mathematics and Mathematical Sciences, Volume 2014, Issue 1, 2014., 2014 Let R ⊂ S be an extension of commutative rings, with X an indeterminate, such that the extension R(X) ⊂ S(X) of Nagata rings has FIP (i.e., S(X) has only finitely many R(X)‐subalgebras). Then, the number of R(X)‐subalgebras of S(X) equals the number of R‐subalgebras of S.
David E. Dobbs +3 more
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A Note on Hobby’s Theorem of Finite Groups
Algebra, Volume 2013, Issue 1, 2013., 2013 It is well known that the Frattini subgroups of any finite groups are nilpotent. If a finite group is not nilpotent, it is not the Frattini subgroup of a finite group. In this paper, we mainly discuss what kind of finite nilpotent groups cannot be the Frattini subgroup of some finite groups and give some results. Moreover, we generalize Hobby’s Theorem.
Qingjun Kong, Ricardo L. Soto
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Seminormal and subnormal subgroup lattices for transitive permutation groups [PDF]
Journal of the Australian Mathematical Society, 2006 AbstractVarious lattices of subgroups of a finite transitive permutation group G can be used to define a set of ‘basic’ permutation groups associated with G that are analogues of composition factors for abstract finite groups. In particular G can be embedded in an iterated wreath product of a chain of its associated basic permutation groups.
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Seminormal graded rings and weakly normal projective varieties
International Journal of Mathematics and Mathematical Sciences, Volume 8, Issue 2, Page 231-240, 1985., 1985 This paper is concerned with the seminormality of reduced graded rings and the weak normality of projective varieties. One motivation for this investigation is the study of the procedure of blowing up a non‐weakly normal variety along its conductor ideal.
John V. Leahy, Marie A. Vitulli
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