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Aims of the project are: 1. Describe the groups of the small order by their endomorphism semigroups. 2. Consider a group as a set on which its endomorphism semigroup (let us call this group a endogroup) is acting. The aim is to study some main properties of abelian endogroups (injectivity, projectivity, flatness). 3. Solve some yet non-solved problems for groups and their endomorphism semigroups (for example: the description of the class of all abelian groups by endomorphism semigroups of groups of this class). |