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On non-Hopfian groups of fractions

Olga Macedońska (2017)

Open Mathematics

The group of fractions of a semigroup S, if exists, can be written as G = SS−1. If S is abelian, then G must be abelian. We say that a semigroup identity is transferable if being satisfied in S it must be satisfied in G = SS−1. One of problems posed by G.Bergman in 1981 asks whether the group G must satisfy every semigroup identity which is satisfied in S, that is whether every semigroup identity is transferable. The first non-transferable identities were constructed in 2005 by S.V.Ivanov and A.M....

On semiabelian groups.

Kuzennyi, N.F., Subbotin, I.Ya. (2005)

International Journal of Mathematics and Mathematical Sciences

On soluble groups of automorphisms of nonorientable Klein surfaces

G. Gromadzki (1992)

Fundamenta Mathematicae

We classify up to topological type nonorientable bordered Klein surfaces with maximal symmetry and soluble automorphism group provided its solubility degree does not exceed 4. Using this classification we show that a soluble group of automorphisms of a nonorientable Riemann surface of algebraic genus q ≥ 2 has at most 24(q-1) elements and that this bound is sharp for infinitely many values of q.

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