It is shown that in a finitely decidable equational class, the solvable radical of any finite subdirectly irreducible member is comparable to all congruences of the irreducible if the type of the monolith is 2. In the type 1 case we establish that the centralizer of the monolith is strongly solvable.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm170-1-4,
author = {Pawe\l\ M. Idziak and Matthew Valeriote},
title = {A property of the solvable radical in finitely decidable varieties},
journal = {Fundamenta Mathematicae},
volume = {167},
year = {2001},
pages = {69-86},
zbl = {0996.08007},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm170-1-4}
}
Paweł M. Idziak; Matthew Valeriote. A property of the solvable radical in finitely decidable varieties. Fundamenta Mathematicae, Tome 167 (2001) pp. 69-86. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm170-1-4/