finite member
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1992 ◽  
Vol 02 (01) ◽  
pp. 89-101 ◽  
Author(s):  
MATTHEW A. VALERIOTE ◽  
ROSS WILLARD

Let [Formula: see text] be a variety whose class of finite members has a decidable first-order theory. We prove that each finite member A of [Formula: see text] satisfies the (3, 1) and (3, 2) transfer principles, and that the minimal sets of prime quotients of type 2 or 3 in A must have empty tails. The first result has already been used by J. Jeong [9] in characterizing the finite subdirectly irreducible members of [Formula: see text] with nonabelian monolith. The second result implies that if [Formula: see text] is also locally finite and omits type 1, then [Formula: see text] is congruence modular.


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