Type 2 subdirectly irreducible algebras in finitely decidable varieties (Q1895585)

A class of algebras is said to be finitely decidable iff its first-order theory is recursive. It is known that if \(V\) is a congruence modular finitely decidable variety and \(A \in V\) is a finite subdirectly irreducible algebra with a type-2 monolith \(\mu\), then (1) the solvable radical \(\nu\) of \(A\) is the centralizer of \(\mu\), (2) \(\nu\) is abelian (i.e. every solvable congruence of \(A\) is abelian), (3) the interval sublattice \(\text{I} [\nu, 1_A] \subseteq \text{Con }A\) is linear, and \(\text{typ} \{\nu, a_A\} \subseteq \{3\}\). The author shows that (1)--(3) hold without the assumption that \(V\) is congruence modular.