Geodesic
On the Boffa alternative
B. Bajorska 1   ; O. Macedońska 1
1 Institute of Mathematics Silesian University of Technology Kaszubska 23 44-100 Gliwice, Poland
Colloquium Mathematicum, Tome 88 (2001) no. 2, pp. 257-261 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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Let $G^*$ denote a nonprincipal ultrapower of a group $G$. In 1986 M.~Boffa posed a question equivalent to the following one: if $G$ does not satisfy a positive law, does $G^*$ contain a free nonabelian subsemigroup? We give the affirmative answer to this question in the large class of groups containing all residually finite and all soluble groups, in fact, all groups considered in traditional textbooks on group theory.
DOI : 10.4064/cm88-2-7
Keywords: * denote nonprincipal ultrapower group boffa posed question equivalent following does satisfy positive law does * contain nonabelian subsemigroup affirmative answer question large class groups containing residually finite soluble groups groups considered traditional textbooks group theory

B. Bajorska  1   ; O. Macedońska  1

1 Institute of Mathematics Silesian University of Technology Kaszubska 23 44-100 Gliwice, Poland 
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B. Bajorska; O. Macedońska. On the Boffa alternative. Colloquium Mathematicum, Tome 88 (2001) no. 2, pp. 257-261. doi: 10.4064/cm88-2-7

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