scholarly journals On finite groups which contain a frobenius factor group

1965 ◽  
Vol 9 (1) ◽  
pp. 47-58 ◽  
Author(s):  
Henry S. Leonard
Keyword(s):  
Finite Groups ◽  
Factor Group

Finite groups which are c-absolute central factor group and the union of Ac-centralizers

2020 ◽  
pp. 2150042
Author(s):  
Esmat Alamshahi ◽  
Mohammad Reza R. Moghaddam ◽  
Farshid Saeedi
Keyword(s):  
Direct Product ◽  
Finite Groups ◽  
Factor Group ◽  
Cyclic Groups ◽  
Central Factor ◽  
Central Factors

Let [Formula: see text] be a group and [Formula: see text] be the [Formula: see text]-absolute center of [Formula: see text], that is, the set of all elements of [Formula: see text] fixed by all class preserving automorphisms of [Formula: see text]. In this paper, we classify all finite groups [Formula: see text], whose [Formula: see text]-absolute central factors are isomorphic to the direct product of cyclic groups, [Formula: see text] and [Formula: see text]. Moreover, we consider finite groups which can be written as the union of centralizers of class preserving automorphisms and study the structure of [Formula: see text] for groups, in which the number of distinct centralizers of class preserving automorphisms is equal to 4 or 5.

On groups satisfying the converse of Lagrange's theorem

1974 ◽  
Vol 75 (1) ◽  
pp. 25-32 ◽  
Author(s):  
J. F. Humphreys
Keyword(s):  
Finite Groups ◽  
Subnormal Subgroup ◽  
Factor Group ◽  
Proved Theorem ◽  
Supersoluble Groups ◽  
Odd Order ◽  
Sylow Tower ◽  
Rank Of A Group ◽  
Lagrange's Theorem

In this article we study certain subclasses of the class ℒ of Lagrangian groups; that is, finite groups G having, for every divisor d of |G|, a subgroup of index d. Two such subclasses, mentioned by McLain in (6), are the class ℒ1 of groups G such that every factor group of G is in ℒ, and the class ℒ2 of groups G such that each subnormal subgroup of G is in ℒ. In section 1 we prove that a group of odd order in ℒ1 is supersoluble, and give some examples of non-supersoluble groups in ℒ1. Section 2 contains several results on the class ℒ2. In particular, it is shown that a group in ℒ2 has an ordered Sylow tower and, after constructing some examples of groups in ℒ2, a result on the rank of a group in ℒ2 is proved (Theorem 4).

scholarly journals On supplements in finite groups

1963 ◽  
Vol 3 (1) ◽  
pp. 63-67
Author(s):  
R. Kochendörffer
Keyword(s):  
Finite Group ◽  
Normal Subgroup ◽  
Finite Groups ◽  
Factor Group ◽  
Extension Theory ◽  
A Finite Group

Let G be a finite group. If N denotes a normal subgroup of G, a subgroup S of G is called a supplement of N if we have G = SN. For every normal subgroup of G there is always the trivial supplement S = G. The existence of a non-trivial supplement is important for the extension theory, i.e., for the description of G by means of N and the factor group G/N. Generally, a supplement S is the more useful the smaller the intersection S ∩ N. If we have even S ∩ N = 1, then S is called a complement for N in G. In this case G is a splitting extension of N by S.

Note on the abstract group (2,3,7;9)

1966 ◽  
Vol 62 (1) ◽  
pp. 7-10 ◽  
Author(s):  
John Leech
Keyword(s):  
Finite Groups ◽  
Factor Group ◽  
Abstract Group ◽  
Image Position

The abstract groupis finite for n = 4,6,7,8, and the relations are incompatible for n = 1,2,3,5. A criterion of Coxeter ((1)) suggests that (2,3,7; n) should be infinite for all n ≥ 9, but its applicability to these groups is unproved, and it is not known whether there are any further examples of finite groups (2,3,7; n). However, (2,3,7; 9) has been proved infinite by Sims ((3)), and it follows at once that (2,3,7; n) is infinite whenever n is a multiple of 9 as it then has an infinite factor group.

scholarly journals Autoclinisms and automorphisms of finite groups II

1980 ◽  
Vol 21 (2) ◽  
pp. 205-207
Author(s):  
Jürgen Tappe
Keyword(s):  
Finite Groups ◽  
Factor Group ◽  
Similar Formula

In part I of this paper P. Hall's formula for finite stem groups was derived. Using results of C. R. Leedham-Green and S. McKay, a similar formula for isoclinic groups with arbitrary branch factor group is shown.The main result of this paper is the following theorem, which appears without proof in [1, p. 203].

FC-Groups whose central factor group can be embedded in a direct product of finite groups

2000 ◽  
Vol 28 (3) ◽  
pp. 1343-1350 ◽  
Author(s):  
L.A. Kurdachenko ◽  
J. Otal ◽  
M.J. Tomkinson
Keyword(s):  
Direct Product ◽  
Finite Groups ◽  
Factor Group ◽  
Central Factor

scholarly journals Products of locally finite groups with min-p

1986 ◽  
Vol 41 (3) ◽  
pp. 352-360 ◽  
Author(s):  
Bernhard Amberg ◽  
Mohammad Reza R. Moghaddam
Keyword(s):  
Finite Groups ◽  
Factor Group ◽  
Locally Finite ◽  
Locally Finite Groups

AbstractThe paper is devoted to showing that if the factorized group G = AB is almost solvable, if A and B are π-subgroups with min-p for some prime p in π and also if the hypercenter factor group A/H(A) or B/H(B) has min p for the prime p. then G is a π-group with min-p for the prime p.

Finite groups with a given absolute central factor group

2014 ◽  
Vol 102 (5) ◽  
pp. 401-409 ◽  
Author(s):  
M. Chaboksavar ◽  
M. Farrokhi Derakhshandeh Ghouchan ◽  
F. Saeedi
Keyword(s):  
Finite Groups ◽  
Factor Group ◽  
Central Factor

Local Root Numbers for Heisenberg-Representations — Some Explicit Results

2020 ◽  
pp. 2050127
Author(s):  
Sazzad Ali Biswas ◽  
Ernst-Wilhelm Zink
Keyword(s):  
Finite Groups ◽  
Abelian Extension ◽  
Factor Group ◽  
Irreducible Representations ◽  
Heisenberg Groups ◽  
Root Number ◽  
Absolute Galois Group ◽  
Root Numbers ◽  
Number Formula ◽  
Local Root

Heisenberg representations [Formula: see text] of (pro-)finite groups [Formula: see text] are by definition irreducible representations of the two-step nilpotent factor group [Formula: see text] Better known are Heisenberg groups which can be understood as allowing faithful Heisenberg representations. A special feature is that [Formula: see text] will be induced by characters [Formula: see text] of subgroups in multiple ways, where the pairs [Formula: see text] can be interpreted as maximal isotropic pairs. If [Formula: see text] is a [Formula: see text]-adic number field and [Formula: see text] the absolute Galois group then maximal isotropic pairs rewrite as [Formula: see text] where [Formula: see text] is an abelian extension and [Formula: see text] a character. We will consider the extended local Artin-root-number [Formula: see text] for those [Formula: see text] which are essentially tame and express it by a formula not depending on the various maximal isotropic pairs [Formula: see text] for [Formula: see text]

scholarly journals Autoclinisms and automorphisms of finite groups II

1980 ◽  
Vol 21 (1) ◽  
pp. 205-207 ◽  
Author(s):  
Jürgen Tappe
Keyword(s):  
Finite Groups ◽  
Factor Group ◽  
Similar Formula

In part I of this paper P. Hall's formula for finite stem groups was derived. Using results of C. R. Leedham-Green and S. McKay, a similar formula for isoclinic groups with arbitrary branch factor group is shown.

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