An example of a finitely defined solvable group without the maximality condition for normal subgroups

1972 ◽  
Vol 12 (3) ◽  
pp. 606-609
Author(s):  
V. N. Remeslennikov
Keyword(s):  
Solvable Group ◽  
Normal Subgroups ◽  
Maximality Condition

On normal subgroups of M-groups

2019 ◽  
Vol 18 (04) ◽  
pp. 1950074
Author(s):  
Xuewu Chang
Keyword(s):  
Normal Subgroup ◽  
Solvable Group ◽  
Solvable Groups ◽  
Hall Subgroup ◽  
Embedding Theorem ◽  
The Other ◽  
Finite Solvable Group ◽  
Embedding Problem ◽  
Normal Subgroups ◽  
Other Hand

The normal embedding problem of finite solvable groups into [Formula: see text]-groups was studied. It was proved that for a finite solvable group [Formula: see text], if [Formula: see text] has a special normal nilpotent Hall subgroup, then [Formula: see text] cannot be a normal subgroup of any [Formula: see text]-group; on the other hand, if [Formula: see text] has a maximal normal subgroup which is an [Formula: see text]-group, then [Formula: see text] can occur as a normal subgroup of an [Formula: see text]-group under some suitable conditions. The results generalize the normal embedding theorem on solvable minimal non-[Formula: see text]-groups to arbitrary [Formula: see text]-groups due to van der Waall, and also cover the famous counterexample given by Dade and van der Waall independently to the Dornhoff’s conjecture which states that normal subgroups of arbitrary [Formula: see text]-groups must be [Formula: see text]-groups.

Groups with a maximality condition for some non-normal subgroups

1995 ◽  
Vol 55 (3) ◽  
pp. 279-292 ◽  
Author(s):  
Giovanni Cutolo ◽  
Leonid A. Kurdachenko
Keyword(s):  
Normal Subgroups ◽  
Maximality Condition

On the supersolvable residual of an M-group

2018 ◽  
Vol 17 (07) ◽  
pp. 1850138
Author(s):  
Huijuan Zheng ◽  
Ping Jin
Keyword(s):  
Solvable Group ◽  
Finite Solvable Group ◽  
Normal Subgroups ◽  
Hall Subgroups

Using the technique of linear limits of characters due to Dade and Loukaki, we give some conditions on the supersolvable residual of a finite solvable group [Formula: see text] that is sufficient to guarantee that [Formula: see text] is an [Formula: see text]-group. The monomiality of normal subgroups and Hall subgroups of the group [Formula: see text] are also determined.

On a class of finite solvable groups

2013 ◽  
Vol 11 (9) ◽  
Author(s):  
James Beidleman ◽  
Hermann Heineken ◽  
Jack Schmidt
Keyword(s):  
Solvable Group ◽  
Prime Order ◽  
Solvable Groups ◽  
Finite Solvable Group ◽  
Normal Subgroups ◽  
Nilpotent Residual ◽  
Quotient Groups ◽  
Subnormal Subgroups

AbstractA finite solvable group G is called an X-group if the subnormal subgroups of G permute with all the system normalizers of G. It is our purpose here to determine some of the properties of X-groups. Subgroups and quotient groups of X-groups are X-groups. Let M and N be normal subgroups of a group G of relatively prime order. If G/M and G/N are X-groups, then G is also an X-group. Let the nilpotent residual L of G be abelian. Then G is an X-group if and only if G acts by conjugation on L as a group of power automorphisms.

scholarly journals Lifts and vertex pairs in solvable groups

2012 ◽  
Vol 55 (1) ◽  
pp. 143-153 ◽  
Author(s):  
James P. Cossey ◽  
Mark L. Lewis
Keyword(s):  
Conjugacy Class ◽  
Solvable Group ◽  
Solvable Groups ◽  
Sufficient Condition ◽  
Normal Subgroups ◽  
Brauer Characters

AbstractSuppose G is a p-solvable group, where p is odd. We explore the connection between lifts of Brauer characters of G and certain local objects in G, called vertex pairs. We show that if χ is a lift, then the vertex pairs of χ form a single conjugacy class. We use this to prove a sufficient condition for a given pair to be a vertex pair of a lift and to study the behaviour of lifts with respect to normal subgroups.

𝒫-characters and the structure of finite solvable groups

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Jiakuan Lu ◽  
Kaisun Wu ◽  
Wei Meng
Keyword(s):  
Finite Group ◽  
Maximal Subgroup ◽  
Solvable Group ◽  
Irreducible Character ◽  
Solvable Groups ◽  
Irreducible Constituent ◽  
A Finite Group

AbstractLet 𝐺 be a finite group. An irreducible character of 𝐺 is called a 𝒫-character if it is an irreducible constituent of (1_{H})^{G} for some maximal subgroup 𝐻 of 𝐺. In this paper, we obtain some conditions for a solvable group 𝐺 to be 𝑝-nilpotent or 𝑝-closed in terms of 𝒫-characters.

scholarly journals On F-Normal Subgroups of Finite Soluble Groups

1995 ◽  
Vol 171 (1) ◽  
pp. 189-203 ◽  
Author(s):  
A. Ballesterbolinches ◽  
K. Doerk ◽  
M.D. Perezramos
Keyword(s):  
Normal Subgroups ◽  
Soluble Groups

scholarly journals Normal subgroups of diffeomorphism and homeomorphism groups of ℝn and other open manifolds

2011 ◽  
Vol 31 (6) ◽  
pp. 1835-1847 ◽  
Author(s):  
PAUL A. SCHWEITZER, S. J.
Keyword(s):  
Normal Subgroup ◽  
Compact Manifold ◽  
Normal Subgroups ◽  
Open Manifold ◽  
Open Manifolds ◽  
Group Of Homeomorphisms ◽  
Homeomorphism Groups

AbstractWe determine all the normal subgroups of the group of Cr diffeomorphisms of ℝn, 1≤r≤∞, except when r=n+1 or n=4, and also of the group of homeomorphisms of ℝn ( r=0). We also study the group A0 of diffeomorphisms of an open manifold M that are isotopic to the identity. If M is the interior of a compact manifold with non-empty boundary, then the quotient of A0 by the normal subgroup of diffeomorphisms that coincide with the identity near to a given end e of M is simple.

Sign in / Sign up

Export Citation Format

Share Document