Hypersubstitutions and Groups
نویسندگان
چکیده
We consider groups as algebras of type (2, 1, 0). A hypersubstitution of type (2, 1, 0) is a mapping σ from the set of the operation symbols {·,−1 , e} into the set of terms of type (2, 1, 0) preserving the arity. For a monoid M of hypersubstitutions of type (2, 1, 0) a variety V is called M -solid if for each group (G; ·,−1 , e) ∈ V the derived group (G; σ(·), σ(−1), σ(e)) also belongs to V for all σ ∈ M . The class S M of all M -solid varieties of groups forms a complete sublattice of the lattice L(Gr) of all varieties of groups. In this way we get a tool for a better description of the whole lattice L(Gr) by characterization of complete sublattices S M . AMS Mathematics Subject Classification (2000): 20M07, 08B15
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