Open AccessAlgorithmic undecidability of recognizing a non-Markovian group property
Author(s) -
V. G. Durnev,
A. I. Zetkina
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1902/1/012061
Subject(s) - group (periodic table) , property (philosophy) , abelian group , mathematics , class (philosophy) , group theory , discrete mathematics , pure mathematics , computer science , physics , quantum mechanics , epistemology , philosophy , artificial intelligence
We prove algorithmic undecidability of the following group property: “the positive theory of a group G coincides with the positive theory of a free non-Abelian group” or (which is equivalent) “the positive theory of a group G coincides with the positive theory of the class of all groups”. This group property is non-Markovian, therefore its algorithmic undecidability does not follow from the fundamental Adyan–Rabin theorem.