Ebook: Foundations of the theory of groupoids and groups

Berlin: VEB Deutscher Verlag der Wissenschaften, 1974 — 215 p.This book contains the foundations of the theory of groupoids and groups. A
groupoid is a nonempty set on which there is defined a binary operation, called
multiplication, associating with every two-membered sequence of elements of the
set again an element of the latter. Generally there are no postulates as regards the
multiplication. The concept of a groupoid forms the basis of an extensive theory of
groupoids which, though rather general, considerably approximates the properties
of groups. The theory of groupoids is founded on the theory of the decompositions
in sets, on the one hand, and on the concept of homomorphic mapping, on the
other hand.