Jordan type of a k[C(p)xC(p)]-module

Date

2011-01-01

Author

Öztürk, Semra

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

273
views

0
downloads

Let E be the elementary abelian group C(p)xC(p), k a field of characteristic p, M a finite dimensional module over the group algebra k[E] and J the Jacobson radical J of k[E]. We prove that the decomposition of M when considered as a k[]-module for a p-point x in J is well defined modulo J(p).

Subject Keywords

Jordan canonical form, Jordan type, Commuting nilpotent matrices, P-points, Shifted cyclic subgroup

URI

https://hdl.handle.net/11511/52850

Journal

NEW YORK JOURNAL OF MATHEMATICS

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

JORDAN TYPES OF COMMUTING NILPOTENT MATRICES Öztürk, Semra (2018-01-01) Let A and B be matrices which are polynomials in r pairwise commuting nilpotent matrices over a field. We give a sufficient condition for the null space of A(i) to equal that of B-i for all i, in particular, for A and B to be similar.
On the index of fixed point subgroup Türkan, Erkan Murat; Ercan, Gülin; Department of Mathematics (2011) Let G be a finite group and A be a subgroup of Aut(G). In this work, we studied the influence of the index of fixed point subgroup of A in G on the structure of G. When A is cyclic, we proved the following: (1) [G,A] is solvable if this index is squarefree and the orders of G and A are coprime. (2) G is solvable if the index of the centralizer of each x in H-G is squarefree where H denotes the semidirect product of G by A. Moreover, for an arbitrary subgroup A of Aut(G) whose order is coprime to the order o...
A GENERALIZED FIXED-POINT-FREE ACTION Güloğlu, İsmail Şuayip; Ercan, Gülin (2013-05-01) In this paper we study the structure of a finite group G admitting a solvable group A of automorphisms of coprime order so that for any x epsilon C-G(A) of prime order or of order 4, every conjugate of x in G is also contained in C-G(A). Under this hypothesis it is proven that the subgroup [G, A] is solvable. Also an upper bound for the nilpotent height of [G, A] in terms of the number of primes dividing the order of A is obtained in the case where A is abelian.
Restricted Modules and Conjectures on Modules of Constant Jordan Type Öztürk, Semra (Springer, 2014-01-01) We introduce the class of restricted k[A]-modules and p t-Jordan types for a finite abelian p-group A of exponent at least p t and a field k of characteristic p. For these modules, we generalize several theorems by Benson, verify a generalization of conjectures stated by Suslin and Rickard giving constraints on Jordan types for modules of constant Jordan type when t is 1. We state conjectures giving constraints on p t-Jordan types and show that many p t-Jordan types are realizable.
RELATIVE GROUP COHOMOLOGY AND THE ORBIT CATEGORY Pamuk, Semra (2014-07-03) Let G be a finite group and F be a family of subgroups of G closed under conjugation and taking subgroups. We consider the question whether there exists a periodic relative F-projective resolution for Z when F is the family of all subgroups HG with rkHrkG-1. We answer this question negatively by calculating the relative group cohomology FH*(G, ?(2)) where G = Z/2xZ/2 and F is the family of cyclic subgroups of G. To do this calculation we first observe that the relative group cohomology FH*(G, M) can be calc...

Citation Formats

S. Öztürk, “Jordan type of a k[C(p)xC(p)]-module,” NEW YORK JOURNAL OF MATHEMATICS, pp. 307–313, 2011, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/52850.