Results 1 to 10 of about 587,234 (53)
A note on groups with a finite number of pairwise permutable seminormal subgroups [PDF]
International Journal of Group Theory, 2022 A subgroup $A$ of a group $G$ is called {\it 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
Alexander Trofimuk
doaj +4 more sources
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
doaj +5 more sources
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
doaj +3 more sources
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.
C. Praeger
openaire +3 more sources
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.
T. Foguel
openaire +2 more sources
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~$G$.
Ballester-Bolinches, A. +3 more
openaire +3 more sources
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
doaj +1 more source
The K-theory of toric varieties in positive characteristic [PDF]
, 2012 We show that if X is a toric scheme over a regular ring containing a field then the direct limit of the K-groups of X taken over any infinite sequence of nontrivial dilations is homotopy invariant. This theorem was known in characteristic 0.
Cortiñas, Guillermo +3 more
core +3 more sources
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
wiley +1 more source
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
wiley +1 more source