Open AccessOn Recognizability of Groups by Bottom Layer
Author(s) -
В. И. Сенашов,
Ivan Parashchuk
Publication year - 2020
Publication title -
advances in modelling and analysis. a, general mathematical and computer tools
Language(s) - English
Resource type - Journals
ISSN - 1258-5769
DOI - 10.18280/ama_a.571-401
Subject(s) - layer (electronics) , pairwise comparison , group (periodic table) , top down and bottom up design , set (abstract data type) , mathematics , combinatorics , prime (order theory) , computer science , chemistry , statistics , materials science , composite material , software engineering , organic chemistry , programming language
The bottom layer of a group is a set of its elements of prime order. A group is called recognizable by bottom layer under additional conditions if it is uniquely restored by bottom layer under these conditions. A group is called almost recognizable by bottom layer under additional conditions, if there are a finite number of pairwise non-isomorphic groups satisfying these conditions, with bottom layer that is the same as that of the group. A group is called unrecognizable by bottom layer under additional conditions if there are an infinite number of pairwise non-isomorphic groups satisfying these conditions, with bottom layer that is the same as that of the group. In the paper we consider examples of groups recognized by bottom layer, by spectrum and, simultaneously, by spectrum and by bottom layer. We have also proved some results of recognizability of groups by bottom layer.