Results 21 to 30 of about 234 (126)
Theoretical Researches about u‐Maximal Subgroups and Its Applications in Charactering IntuG
Journal of Chemistry, Volume 2019, Issue 1, 2019., 2019 Let G be a finite group and u be the class of all finite supersoluble groups. A supersoluble subgroup U of G is called u‐maximal in G if for any supersoluble subgroup V of G containing U, V = U. Moreover, IntuG is the intersection of all u‐maximal subgroups of G.
Li Zhang, Zheng-Qun Cai, Shaohui Wang
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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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On p-supersolvability of finite groups
Proceedings - Mathematical Sciences, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Converse Lagrange theorem orders and supersolvable orders [PDF]
, 2021 For finite groups, we investigate both converse Lagrange theorem (CLT) orders and supersolvable (SS) orders, and see that the latter form a proper subset of the former.
Manning, Joseph, MacHale, Desmond
core
On supersolvability of finite groups [PDF]
Glasgow Mathematical Journal, 2001 We prove a natural factorization of supersolvable groups and then we give another characterization of them in connection with the Fitting subgroup. Applying these theorems we describe the structure of some subclasses of supersolvable groups.
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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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A note on finite group structure influenced by second and third maximal subgroups
International Journal of Mathematics and Mathematical Sciences, Volume 13, Issue 4, Page 747-750, 1990., 1990 The structure of a finite group having specified number of second and third maximal subgroups has been investigated in the paper.
N. P. Mukherjee, R. Khazal
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