The Fitting Subgroup of Some Just non-$\mathcal{X}$-Groups

2002 ◽  
pp. 109-113
Keyword(s):  
Fitting Subgroup

scholarly journals Maximal subgroups of finite groups

1990 ◽  
Vol 13 (2) ◽  
pp. 311-314
Author(s):  
S. Srinivasan
Keyword(s):  
Maximal Subgroup ◽  
Finite Groups ◽  
Maximal Subgroups ◽  
Fitting Subgroup ◽  
Small Index

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 subgroup of the group.

scholarly journals The p-Huppert-subgroup and the set of p-quasi-superfluous elements in a finite group

1993 ◽  
Vol 36 (2) ◽  
pp. 289-297
Author(s):  
Angel Carocca ◽  
Rudolf Maier
Keyword(s):  
Finite Group ◽  
Normal Subgroup ◽  
Prime Number ◽  
Special Interest ◽  
Fitting Subgroup ◽  
Supersoluble Groups ◽  
A Finite Group ◽  
Parametrized Family

Based on the theory of p-supersoluble and supersoluble groups, a prime-number parametrized family of canonical characteristic subgroups Γp(G) and their intersection Γ(G) is introduced in every finite group G and some of its properties are studied. Special interest is dedicated to an elementwise description of the largest p-nilpotent normal subgroup of Γp(G) and of the Fitting subgroup of Γ(G).

Generalized Fitting subgroup of a group of finite Morley rank

1991 ◽  
Vol 56 (4) ◽  
pp. 1391-1399 ◽  
Author(s):  
Ali Nesin
Keyword(s):  
Finite Group ◽  
Morley Rank ◽  
Fitting Subgroup ◽  
Generalized Fitting Subgroup ◽  
Finite Morley Rank ◽  
The Generalized Fitting Subgroup ◽  
A Finite Group ◽  
Subnormal Subgroups

AbstractWe define a characteristic and definable subgroup F*(G) of any group G of finite Morley rank that behaves very much like the generalized Fitting subgroup of a finite group. We also prove that semisimple subnormal subgroups of G are all definable and that there are finitely many of them.

Solvable groups with restrictions on Sylow subgroups of the Fitting subgroup

2016 ◽  
Vol 09 (02) ◽  
pp. 1650037
Author(s):  
Alexander Trofimuk
Keyword(s):  
Free Groups ◽  
Solvable Groups ◽  
Fitting Subgroup ◽  
Sylow Subgroups ◽  
Nilpotent Length ◽  
Derived Length ◽  
Odd Order

In this paper, we study solvable groups in which [Formula: see text] is at most 2. In particular, we investigated groups of odd order and [Formula: see text]-free groups with this property. Exact estimations of the derived length and nilpotent length of such groups are obtained.

On Finite Soluble Groups

1969 ◽  
Vol 9 (1-2) ◽  
pp. 250-251 ◽  
Author(s):  
J. N. Ward
Keyword(s):  
Normal Subgroup ◽  
Minimal Normal Subgroup ◽  
Saturated Formation ◽  
Fitting Subgroup ◽  
Minimal Order ◽  
Soluble Groups

Let p be a class of finite soluble groups which is closed under epimorphic images and let g be a saturated formation. Then if G is a group of minimal order belonging to p but not to g, F(G), the Fitting subgroup of G, is the unique minimal normal subgroup of G. It is to groups with this property that the following proposition is applicable.

Finite soluble groups admitting an automorphism of prime power order with few fixed points

1987 ◽  
Vol 102 (3) ◽  
pp. 431-441 ◽  
Author(s):  
Brian Hartley ◽  
Volker Turau
Keyword(s):  
Fixed Points ◽  
Soluble Group ◽  
Prime Power ◽  
Prime Power Order ◽  
Finite Soluble Group ◽  
Prime Divisors ◽  
Fitting Subgroup ◽  
Soluble Groups ◽  
Fitting Height ◽  
Number Of Prime Divisors

Let G be a finite soluble group with Fitting subgroup F(G). The Fitting series of G is defined, as usual, by F0(G) = 1 and Fi(G)/Fi−1(G) = F(G/Fi−1(G)) for i ≥ 1, and the Fitting height h = h(G) of G is the least integer such that Fn(G) = G. Suppose now that a finite soluble group A acts on G. Let k be the composition length of A, that is, the number of prime divisors (counting multiplicities) of |A|. There is a certain amount of evidence in favour of theCONJECTURE. |G:Fk(G)| is bounded by a number depending only on |A| and |CG(A)|.

scholarly journals Finitep′-nilpotent groups. I

1987 ◽  
Vol 10 (1) ◽  
pp. 135-146 ◽  
Author(s):  
S. Srinivasan
Keyword(s):  
Nilpotent Group ◽  
Nilpotent Groups ◽  
Fitting Subgroup ◽  
Frattini Subgroup

In this paper we consider finitep′-nilpotent groups which is a generalization of finitep-nilpotent groups. This generalization leads us to consider the various special subgroups such as the Frattini subgroup, Fitting subgroup, and the hypercenter in this generalized setting. The paper also considers the conditions under which product ofp′-nilpotent groups will be ap′-nilpotent group.

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