Complementability conditions for a periodic almost solvable subgroup in the group containing it

1992 ◽  
Vol 44 (6) ◽  
pp. 741-745
Author(s):  
S. N. Chernikov ◽  
N. S. Chernikov
Keyword(s):  
Solvable Subgroup

scholarly journals Solvable Subgroup Theorem for simplicial nonpositive curvature

2018 ◽  
Vol 28 (04) ◽  
pp. 605-611
Author(s):  
Tomasz Prytuła
Keyword(s):  
Nonpositive Curvature ◽  
Decomposition Theorem ◽  
Solvable Subgroup ◽  
Finitely Generated ◽  
Flat Torus ◽  
Product Decomposition ◽  
Subgroup Theorem

Given a group [Formula: see text] with bounded torsion that acts properly on a systolic complex, we show that every solvable subgroup of [Formula: see text] is finitely generated and virtually abelian of rank at most [Formula: see text]. In particular, this gives a new proof of the above theorem for systolic groups. The main tools used in the proof are the Product Decomposition Theorem and the Flat Torus Theorem.

scholarly journals Kernel systems on finite groups

2001 ◽  
Vol 163 ◽  
pp. 71-85 ◽  
Author(s):  
Paul Lescot
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Prime Factor ◽  
A Priori ◽  
Solvable Subgroup ◽  
Natural Conditions ◽  
Sylow Subgroups ◽  
Frobenius Kernel ◽  
Maximal Solvable Subgroup

We introduce a notion of kernel systems on finite groups: roughly speaking, a kernel system on the finite group G consists in the data of a pseudo-Frobenius kernel in each maximal solvable subgroup of G, subject to certain natural conditions. In particular, each finite CA-group can be equipped with a canonical kernel system. We succeed in determining all finite groups with kernel system that also possess a Hall p′-subgroup for some prime factor p of their order; this generalizes a previous result of ours (Communications in Algebra 18(3), 1990, pp. 833-838). Remarkable is the fact that we make no a priori abelianness hypothesis on the Sylow subgroups.

Solvable and Nilpotent Subgroups of GL(n,qm)

1982 ◽  
Vol 34 (5) ◽  
pp. 1097-1111 ◽  
Author(s):  
Thomas R. Wolf
Keyword(s):  
Finite Field ◽  
Vector Space ◽  
Solvable Subgroup ◽  
Linear Transformations ◽  
Completely Reducible ◽  
Image Position

Let V ≠ 0 be a vector space of dimension n over a finite field of order qm for a prime q. Of course, GL(n, qm) denotes the group of -linear transformations of V. With few exceptions, GL(n, qm) is non-solvable. How large can a solvable subgroup of GL(n, qm) be? The order of a Sylow-q-subgroup Q of GL(n, qm) is easily computed. But Q cannot act irreducibly nor completely reducibly on V.Suppose that G is a solvable, completely reducible subgroup of GL(n, qm). Huppert ([9], Satz 13, Satz 14) bounds the order of a Sylow-q-subgroup of G, and Dixon ([5], Corollary 1) improves Huppert's bound. Here, we show that |G| ≦ q3nm = |V|3. In fact, we show thatwhere

scholarly journals Translation planes of odd order and odd dimension

1979 ◽  
Vol 2 (2) ◽  
pp. 187-208 ◽  
Author(s):  
T. G. Ostrom
Keyword(s):  
Vector Space ◽  
Finite Groups ◽  
Translation Planes ◽  
Solvable Subgroup ◽  
Joint Paper ◽  
Desarguesian Planes ◽  
Odd Order ◽  
Collineation Groups ◽  
Zero Vector

The author considers one of the main problems in finite translation planes to be the identification of the abstract groups which can act as collineation groups and how those groups can act.The paper is concerned with the case where the plane is defined on a vector space of dimension2d overGF(q), whereqanddare odd. If the stabilizer of the zero vector is non-solvable, letG0be a minimal normal non-solvable subgroup. We suspect thatG0must be isomorphic to someSL(2,u)or homomorphic toA6orA7. Our main result is that this is the case whendis the product of distinct primes.The results depend heavily on the Gorenstein-Walter determination of finite groups having dihedral Sylow2-groups whendandqare both odd. The methods and results overlap those in a joint paper by Kallaher and the author which is to appear in Geometriae Dedicata. The only known example (besides Desarguesian planes) is Hering's plane of order27(i.e.,dandqare both equal to3) which admitsSL(2,13).

scholarly journals Integrability of doubly-periodic Riccati equation

1998 ◽  
Vol 21 (4) ◽  
pp. 785-790 ◽  
Author(s):  
Ma Ling ◽  
Guan Ke-Ying
Keyword(s):  
Riccati Equation ◽  
Elliptic Function ◽  
Solvable Subgroup ◽  
Function Coefficient ◽  
Fuchsian Equation

By the structure of solvable subgroup ofSL(2,ℂ)(see [1]), the integrability and properties of solutions of a Riccati equation with an elliptic function coefficient, which is related to a Fuchsian equation on the torusT2,is studied.

THE BINARY ADDING MACHINE AND SOLVABLE GROUPS

2003 ◽  
Vol 13 (01) ◽  
pp. 95-110
Author(s):  
SAID SIDKI
Keyword(s):  
Binary Tree ◽  
Metabelian Group ◽  
Solvable Groups ◽  
Solvable Subgroup ◽  
Free Metabelian Group ◽  
Torsion Free

We prove that any solvable subgroup K of automorphisms of the binary tree, which contains the binary adding machine is an extension of a torsion-free metabelian group by a finite 2-group. If the group K is moreover nilpotent then it is torsion-free abelian.

Locality of solvable subgroup-closed Fitting classes

1992 ◽  
Vol 51 (3) ◽  
pp. 221-225 ◽  
Author(s):  
N. T. Vorob'ev
Keyword(s):  
Solvable Subgroup ◽  
Fitting Classes
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