The theories of V. V. Wagner (1908-1981) on abstractions of systems of
binary relations are presented here within their historical and
mathematical contexts. This book contains the first translation from
Russian into English of a selection of Wagner's papers, the ideas of
which are connected to present-day mathematical research. Along with a
translation of Wagner's main work in this area, his 1953 paper 'Theory
of generalised heaps and generalised groups, ' the book also includes
translations of three short precursor articles that provide additional
context for his major work.
Researchers and students interested in both algebra (in particular,
heaps, semiheaps, generalised heaps, semigroups, and groups) and
differential geometry will benefit from the techniques offered by these
translations, owing to the natural connections between generalised heaps
and generalised groups, and the role played by these concepts in
differential geometry. This book gives examples from present-day
mathematics where ideas related to Wagner's have found fruitful
applications.