Abstract.
We determine the dominion (in the sense of Isbell) of a subgroup H of a finite nonabelian simple group S in Var(S). We also obtain necessary and suficient conditions for H to be epimorphically embedded in S, and derive several examples, which generalize an example of B. H. Neumann. Finally, we extend the results to a variety generated by a family of finite nonabelian simple groups.
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Received May 12, 1999; accepted in final form April 9, 2002.
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Magidin, A. Dominions in varieties generated by simple groups. Algebra univers. 48, 133–143 (2002). https://doi.org/10.1007/PL00012445
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DOI: https://doi.org/10.1007/PL00012445