Group and semigroup theoretic considerations inspired by inverse problems of the additive number theory
This paper contains an expanded version of a talk on algebraic systems with small squaring given by the first author during the traditional Mathematical Colloquium at the University of St. Andrews, Scotland, in the summer of 1984. New results for groups and semigroups are added. The collaboration of the authors on these topics started in Kääriku, Estonia, in 1976, continued in Moscow, Russia, in 1977–1979, in St. Andrews, Scotland, in 1984, Fayetteville, Arkansas, in 1985, and Tel-Aviv, Israel, in 1986. The authors are grateful to Graham Higman, Joseph Rotman and Elliot Weinberg for fruitful discussions.
KeywordsLeft Identity Commutative Semigroup Quaternion Group Left Coset Zero Semigroup
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