On the Absence of Cohomological Finiteness in Wreath Products

Graph-wreath products and finiteness conditionsI

A notion of graph-wreath product of groups is introduced. We obtain sufficient conditions for these products to satisfy the topologically inspired finiteness condition type Fn. Under various additional assumptions we show that these conditions are necessary. Our results generalize results of Bartholdi, Cornulier and Kochloukova about wreath products. Graphwreath products of groups include class...

UPPER BOUNDS FOR FINITENESS OF GENERALIZED LOCAL COHOMOLOGY MODULES

Let $R$ be a commutative Noetherian ring with non-zero identity and $fa$ an ideal of $R$. Let $M$ be a finite $R$--module of finite projective dimension and $N$ an arbitrary finite $R$--module. We characterize the membership of the generalized local cohomology modules $lc^{i}_{fa}(M,N)$ in certain Serre subcategories of the category of modules from upper bounds. We define and study the properti...

On Finite Generation and Other Finiteness Conditions for Wreath Products of Semigroups

Restricted cascade and wreath products of fuzzy finite switchboard state machines

A finite switchboard state machine is a specialized finite state machine. It is built by binding the concepts of switching state machines and commutative state machines. The main purpose of this paper is to give a specific algorithm for fuzzy finite switchboard state machine and also, investigates the concepts of switching relation, covering, restricted cascade products and wreath products of f...

Deciding the finiteness of the number of simple permutations contained in a wreath-closed class is polynomial

We present an algorithm running in time O(n logn) which decides if a wreathclosed permutation class Av(B) given by its finite basis B contains a finite number of simple permutations. The method we use is based on an article of Brignall, Ruškuc and Vatter [9] which presents a decision procedure (of high complexity) for solving this question, without the assumption that Av(B) is wreath-closed. Us...