About the decomposability of almost completely decomposable groups

Download

12625625.pdf

Date

2020-8

Author

Budak, Canan

Metadata

Show full item record

Item Usage Stats

320
views

184
downloads

Almost completely decomposable groups are extensions of completely decomposable groups of finite index. They can be written as a sum of indecomposables. Every almost completely decomposable group is the direct sum of indecomposables but this decomposition is quite complicated and not unique. Almost completely decomposable groups can be represented by matrices, called coordinate matrices. If the coordinate matrix of a given almost completely decomposable group is decomposable then the group is decomposable. Under some restrictions, for example considering a weakening of isomorphism, called near-isomorphism some spacial classes of almost completely decomposable groups can be classified.

Subject Keywords

Acd groups, Torsion free groups, Decomposability of acd groups

URI

https://hdl.handle.net/11511/69045

Collections

Graduate School of Natural and Applied Sciences, Thesis

Suggestions

OpenMETU
Core

Description of Barely Transitive Groups with Soluble Point Stabilizer Betin, Cansu; Kuzucuoğlu, Mahmut (Informa UK Limited, 2009-6-4) We describe the barely transitive groups with abelian-by-finite, nilpotent-by-finite and soluble-by-finite point stabilizer. In article [6] Hartley asked whether there is a torsionfree barely transitive group. One consequence of our results is that there is no torsionfree barely transitive group whose point stabilizer is nilpotent. Moreover, we show that if the stabilizer of a point is a permutable subgroup of an infinitely generated barely transitive group G, then G is locally finite.
Universal groups of intermediate growth and their invariant random subgroups Benli, Mustafa Gökhan; Nagnibeda, Tatiana (2015-07-01) We exhibit examples of groups of intermediate growth with ergodic continuous invariant random subgroups. The examples are the universal groups associated with a family of groups of intermediate growth.
Beauville structures in p-groups Gül, Şükran; Ercan, Gülin; Fernández-Alcober, Gustavo Adolfo; Department of Mathematics (2016) Given a finite group G and two elements x, y in G, we denote by Sigma(x,y) the union of all conjugates of the cyclic subgroups generated by x, y and xy. Then G is called a Beauville group of unmixed type if the following conditions hold: (i) G is a 2-generator group. (ii) G has two generating sets {x1,y1} and {x2, y2} such that Sigma (x1, y1) intersection Sigma(x2, y2) is 1. In this case, {x1, y1} and {x2, y2} are said to form a Beauville structure for G. The main purpose of this thesis is to extend the kn...
The Influence of some embedding properties of subgroups on the structure of a finite group Kızmaz, Muhammet Yasir; Ercan, Gülin; Department of Mathematics (2018) In a finite group $G$, a subgroup $H$ is called a $TI$-subgroup if $H$ intersects trivially with distinct conjugates of itself. Suppose that $H$ is a Hall $pi$-subgroup of $G$ which is also a $TI$-subgroup. A famous theorem of Frobenius states that $G$ has a normal $pi$-complement whenever $H$ is self normalizing. In this case, $H$ is called a Frobenius complement and $G$ is said to be a Frobenius group. A first main result in this thesis is the following generalization of Frobenius' Theorem. textbf{Theorem...
Fixed point free action on groups of odd order Ercan, Gülin; Güloğlu, İsmail Ş. (Elsevier BV, 2008-7) Let A be a finite abelian group that acts fixed point freely on a finite (solvable) group G. Assume that |G| is odd and A is of squarefree exponent coprime to 6. We show that the Fitting length of G is bounded by the length of the longest chain of subgroups of A.

Citation Formats

C. Budak, “About the decomposability of almost completely decomposable groups,” M.S. - Master of Science, Middle East Technical University, 2020.