The efficiency of standard wreath product

Abstract

Let £ be the set of all finite groups that have efficient presentations. In this paper we give sufficient conditions for the standard wreath product of two ^-groups to be a £-group.

How effects efficiency on the word problem for monoids?

“…There are some key studies on them. We may refer [4] and citations in it for the definitions and fundamental properties of them. At this point, we should remark that these properties need to be defined on the minimal number of generators to ensure a health classification.…”

“…Let us remind these algebraic properties. For a monoid presentation P, the efficiency is defined as in the following ( [4]).…”

“…Let M be a monoid with a presentation P = [Y, S] . Then the Euler characteristic (see, [4,5]) of P is defined by χ(P) = 1 − |Y| + |S| , where |.| denotes the minimal number of elements in the set. Also, we have a bound-parameter other than Euler characteristic which is related to the efficiency, namely homological bound δ(M).…”

Knit Products of Some Groups and Their Applications

“…A brief survey of known results on efficiency can be found in [6]. In fact there is interest not only in finding efficient presentations, but also finding presentations which are efficient on the minimal number of generators (see [19]).…”

One dimension higher of the word problem

“…Thus one can generate the above theorem to the global properties such as the p-Cockcroft properties or the efficiency. The reader can find the details and some applications of the p-Cockcroft property and the efficiency, for instance, in [6], [7].…”