CHARACTERIZATION OF A SEMIDIRECT PRODUCT OF GROUPS BY ITS ENDOMORPHISM SEMIGROUP

Semigroups ◽  
2000 ◽  
Author(s):  
PEETER PUUSEMP
Keyword(s):  
Semidirect Product ◽  
Endomorphism Semigroup ◽  
Product Of Groups

scholarly journals Supramenable groups and partial actions

2016 ◽  
Vol 37 (5) ◽  
pp. 1592-1606 ◽  
Author(s):  
EDUARDO P. SCARPARO
Keyword(s):  
Semidirect Product ◽  
Crossed Product ◽  
Probability Measures ◽  
Crossed Products ◽  
Hausdorff Spaces ◽  
Tracial States ◽  
Product Of Groups

We characterize supramenable groups in terms of the existence of invariant probability measures for partial actions on compact Hausdorff spaces and the existence of tracial states on partial crossed products. These characterizations show that, in general, one cannot decompose a partial crossed product of a $\text{C}^{\ast }$-algebra by a semidirect product of groups into two iterated partial crossed products. However, we give conditions which ensure that such decomposition is possible.

SEMIDIRECT PRODUCTS IN ALGEBRAIC LOGIC AND SOLUTIONS OF THE QUANTUM YANG–BAXTER EQUATION

2008 ◽  
Vol 07 (04) ◽  
pp. 471-490 ◽  
Author(s):  
WOLFGANG RUMP
Keyword(s):  
Semidirect Product ◽  
Binary Operation ◽  
Algebraic Logic ◽  
Type Theorem ◽  
Combinatorial Theory ◽  
Baxter Equation ◽  
Semidirect Products ◽  
Special Classes

A semidirect product is introduced for cycloids, i.e. sets with a binary operation satisfying (x · y) · (x · z) = (y · x) · (y · z). Special classes of cycloids arise in the combinatorial theory of the quantum Yang–Baxter equation, and in algebraic logic. In the first instance, semidirect products can be used to construct new solutions of the quantum Yang–Baxter equation, while in algebraic logic, they lead to a characterization of L-algebras satisfying a general Glivenko type theorem.

scholarly journals Is a semidirect product of groups necessarily a group?

1993 ◽  
Vol 118 (3) ◽  
pp. 689-689 ◽  
Author(s):  
Gary F. Birkenmeier ◽  
C. Brad Davis ◽  
Kevin J. Reeves ◽  
Sihai Xiao
Keyword(s):  
Semidirect Product ◽  
Product Of Groups

Left-invariant almost α-coKähler structures on 3D semidirect product Lie groups

2019 ◽  
Vol 16 (01) ◽  
pp. 1950011 ◽  
Author(s):  
Domenico Perrone
Keyword(s):  
Lie Groups ◽  
Semidirect Product ◽  
Three Dimensional ◽  
Reeb Vector ◽  
Reeb Vector Field ◽  
The Matrix ◽  
Canonical Foliation ◽  
Matrix Formula ◽  
Simply Connected

The main result of this paper gives a characterization of left-invariant almost [Formula: see text]-coKähler structures on three-dimensional (3D) semidirect product Lie groups [Formula: see text] in terms of the matrix [Formula: see text]. Then, we study the harmonicity of the Reeb vector field [Formula: see text] of a simply connected homogeneous almost [Formula: see text]-coKähler three-manifold, in terms of the Gaussian curvature of the canonical foliation.

scholarly journals The Schur-Zassenhaus theorem in locally finite groups

1976 ◽  
Vol 22 (4) ◽  
pp. 491-493 ◽  
Author(s):  
B. Hartley
Keyword(s):  
Semidirect Product ◽  
Finite Index ◽  
Finite Groups ◽  
Subdirect Product ◽  
Locally Finite ◽  
Locally Finite Groups ◽  
Countable Case

AbstractLet L = HK be a semidirect product of a normal locally finite π′-group H by a locally finite π′-group K, where π, is a set of primes. Suppose CK(H) = 1 and L is Sylow π-sparse (which in the countable case just says that the Sylow π-subgroups of L are conjugate). This paper completes the characterization of those groups which can occur as K—this had previously been obtained under the assumption that L is locally soluble. The answer is the same—essentially that the groups occurring are those having a subgroup of finite index which is a subdirect product of so-called “pinched” groups.

scholarly journals A CHARACTERIZATION OF SCHMIDT GROUPS BY THEIR ENDOMORPHISM SEMIGROUPS

2005 ◽  
Vol 15 (01) ◽  
pp. 161-173 ◽  
Author(s):  
PEETER PUUSEMP
Keyword(s):  
Finite Group ◽  
Solvable Group ◽  
Semidirect Product ◽  
Proper Subgroup ◽  
Schmidt Group

A Schmidt group is a non-nilpotent finite group in which each proper subgroup is nilpotent. Each Schmidt group G is a solvable group of order ps qv (where p and q are different primes) with a unique Sylow p-subgroup P and a cyclic Sylow q-subgroup Q, and hence G is a semidirect product of P by Q. Denote by [Formula: see text] the class of all Schmidt groups of orders ps qv, where p, q, and v are fixed and s is arbitrary. It is shown in this paper that the class [Formula: see text] can be characterized by the properties of the endomorphism semigroups of the groups of this class. It follows from this characterization that if [Formula: see text] and H is another group such that the endomorphism semigroups of G and H are isomorphic, then [Formula: see text], too.

Application of the Semidirect Product of Groups

1971 ◽  
Vol 12 (2) ◽  
pp. 314-314 ◽  
Author(s):  
Robert Geroch ◽  
E. T. Newman
Keyword(s):  
Semidirect Product ◽  
Product Of Groups
Sign in / Sign up

Export Citation Format

Share Document