Results 11 to 20 of about 94 (79)
On Quasi S‐Propermutable Subgroups of Finite Groups
Journal of Mathematics, Volume 2020, Issue 1, 2020., 2020 A subgroup H of a finite group G is said to be quasi S‐propermutable in G if K⊲¯G such that HK is S‐permutable in G and H ∩ K ≤ HqsG, where HqsG is the subgroup formed by all those subgroups of H which are S‐propermutable in G. In this paper, we give some generalizations of finite group G by using the properties and effects of quasi S‐propermutable ...
Hong Yang +6 more
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Two Generator Subalgebras Of Lie Algebras. [PDF]
, 2007 In [14] Thompson showed that a finite group G is solvable if and only if every twogenerated subgroup is solvable (Corollary 2, p. 388). Recently, Grunevald et al.
Kevin Bowman +5 more
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On solvable groups with one vanishing class size [PDF]
, 2020 Let G be a finite group, and let cs(G) be the set of conjugacy class sizes of G. Recalling that an element g of G is called a vanishing element if there exists an irreducible character of G taking the value 0 on g, we consider one particular subset of cs(
E. Pacifici +3 more
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A Note on the Normal Index and the c‐Section of Maximal Subgroups of a Finite Group
Journal of Applied Mathematics, Volume 2014, Issue 1, 2014., 2014 Let M be a maximal subgroup of finite group G. For each chief factor H/K of G such that K ≤ M and G = MH, we called the order of H/K the normal index of M and (M∩H)/K a section of M in G. Using the concepts of normal index and c‐section, we obtain some new characterizations of p‐solvable, 2‐supersolvable, and p‐nilpotent.
Na Tang, Xianhua Li, Junjie Wei
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Finite Groups with Some SE‐Supplemented Subgroups
Algebra, Volume 2013, Issue 1, 2013., 2013 Let H be a subgroup of a finite group G, p a prime dividing the order of G, and P a Sylow p‐subgroup of G for prime p. We say that H is SE‐supplemented in G if there is a subgroup K of G such that G = HK and H∩K ≤ HseG, where HseG denotes the subgroup of H generated by all those subgroups of H which are S‐quasinormally embedded in G.
Guo Zhong +5 more
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Finite Groups Whose Certain Subgroups of Prime Power Order Are S‐Semipermutable
International Scholarly Research Notices, Volume 2011, Issue 1, 2011., 2011 Let G be a finite group. A subgroup H of G is said to be S‐semipermutable in G if H permutes with every Sylow p‐subgroup of G with (p, |H|) = 1. In this paper, we study the influence of S‐permutability property of certain abelian subgroups of prime power order of a finite group on its structure.
Mustafa Obaid, A. Kiliçman
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Mutually Permutable Products of Finite Groups
International Scholarly Research Notices, Volume 2011, Issue 1, 2011., 2011 Let G be a finite group and G1, G2 are two subgroups of G. We say that G1 and G2 are mutually permutable if G1 is permutable with every subgroup of G2 and G2 is permutable with every subgroup of G1. We prove that if G = G1G2 = G1G3 = G2G3 is the product of three supersolvable subgroups G1, G2, and G3, where Gi and Gj are mutually permutable for all i ...
Rola A. Hijazi +4 more
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Finite groups whose set of numbers of subgroups of possible order has exactly 2 elements [PDF]
, 2014 summary:Counting subgroups of finite groups is one of the most important topics in finite group theory. We classify the finite non-nilpotent groups $G$ whose set of numbers of subgroups of possible orders $n(G)$ has exactly two elements. We show that if $
Shao, Changguo, Jiang, Qinhui
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A note on p‐solvable and solvable finite groups
International Journal of Mathematics and Mathematical Sciences, Volume 17, Issue 4, Page 821-824, 1994., 1994 The notion of normal index is utilized in proving necessary and sufficient conditions for a group G to be respectively, p‐solvable and solvable where p is the largest prime divisor of |G|. These are used further in identifying the largest normal p‐solvable and normal solvable subgroups, respectively, of G.
R. Khazal, N. P. Mukherjee
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Maximal subgroups of finite groups
International Journal of Mathematics and Mathematical Sciences, Volume 13, Issue 2, Page 311-314, 1990., 1989 In finite groups maximal subgroups play a very important role. Results in the literature show that if the maximal subgroup has a very small index in the whole group then it influences the structure of the group itself. In this paper we study the case when the index of the maximal subgroups of the groups have a special type of relation with the Fitting ...
S. Srinivasan
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