Results 21 to 30 of about 5,389,809 (116)
CONSTRUCTION OF TRANSITIVE SUPERSOLVABLE PERMUTATION GROUPS [PDF]
, 2018 In this paper, we used wreath products of two permutation groups in constructing transitive supersolvable permutation groups. We verified these groups using some groups theoretical concepts and also validate our work using a standard program; GAP ...
Musa, Sani +3 more
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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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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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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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On p-supersolvability of finite groups
Proceedings - Mathematical Sciences, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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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Irreducible representations of semisimple algebraic groups and supersolvable lattices [PDF]
, 2012 Let Λ be the cross section lattice of an irreducible representation of a semisimple algebraic group. Certain combinatorial properties of Λ are studied. Supersolvable Λʼs are determined in terms of Dynkin diagrams.
Can, Mahir Bilen, Mahir Bilen Can
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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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