Group identities on the units of algebraic algebras with applications to restricted enveloping algebras
E Jespers, D Riley, S Siciliano - arXiv preprint math/0701690, 2007 - arxiv.org
E Jespers, D Riley, S Siciliano
arXiv preprint math/0701690, 2007•arxiv.org… As evidence for a positive solution, we offer the fact proved in [8] that every group algebra
of a periodically generated group over an infinite field is locally finite provided its group of
units satisfies a group identity. We shall offer presently some additional support to Problem
1.3 in the case of nilpotently generated algebras. The case when the base field is infinite
was settled positively by Theorem 1.2 in [6]. Finally, in the last section, we apply our general
results to the special case when the algebra in question is the restricted enveloping algebra …
of a periodically generated group over an infinite field is locally finite provided its group of
units satisfies a group identity. We shall offer presently some additional support to Problem
1.3 in the case of nilpotently generated algebras. The case when the base field is infinite
was settled positively by Theorem 1.2 in [6]. Finally, in the last section, we apply our general
results to the special case when the algebra in question is the restricted enveloping algebra …
An algebra is called a GI-algebra if its group of units satisfies a group identity. We provide positive support for the following two open problems. 1. Does every algebraic GI-algebra satisfy a polynomial identity? 2. Is every algebraically generated GI-algebra locally finite?
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