Results 1 to 10 of about 494 (47)
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
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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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Subnormal, permutable, and embedded subgroups in finite groups
Open Mathematics, 2011 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.
Beidleman James, Ragland Mathew
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On the Supersoluble Residual of a Product of Supersoluble Subgroups [PDF]
Advances in Group Theory and Applications, 2020 Let P be the set of all primes. A subgroup H of a group G is called P-subnormal in G, if either H = G, or there exists a chain of subgroups H = H_0 \leq H_1 \leq ... \leq H_n = G, with |H_i : H_{i-1}| \in P for all i.
Victor S. Monakhov +1 more
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$4$-quasinormal subgroups of prime order [PDF]
International Journal of Group Theory, 2020 Generalizing the concept of quasinormality, a subgroup $H$ of a group $G$ is said to be 4-quasinormal in $G$ if, for all cyclic subgroups $K$ of $G$, $\langle H,K\rangle=HKHK$.
Stewart Stonehewer
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Finite Groups whose Cyclic Subnormal Subgroups Satisfy Certain Permutability Conditions [PDF]
Advances in Group Theory and Applications, 2016 Finite groups in which each cyclic subnormal subgroup is semipermutable, S-semipermutable or seminormal are investigated.
A. Ballester-Bolinches +2 more
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Some New Local Properties Defining Soluble PST-Groups [PDF]
Advances in Group Theory and Applications, 2017 Let $G$ be a group and $p$ a prime number. $G$ is said to be a $Y_p$-group if whenever $K$ is a $p$-subgroup of $G$ every subgroup of $K$ is an $S$-permutable subgroup in $N_G(K)$.
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~$G$.
Ballester-Bolinches, A. +3 more
openaire +2 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
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