On just-infiniteness of locally finite groups and their C*-algebras
V. Belyaev, R. Grigorchuk, P. Shumyatsky

TL;DR
This paper constructs a family of locally finite residually finite groups with just-infinite C*-algebras, answering an open question, and proves that residually finite groups of finite exponent are not just-infinite.
Contribution
It introduces a new family of groups with specific C*-algebra properties and clarifies the limitations of residually finite groups of finite exponent.
Findings
Constructed locally finite residually finite groups with just-infinite C*-algebras
Proved residually finite groups of finite exponent are not just-infinite
Answered an open question from prior research
Abstract
We give a construction of a family of locally finite residually finite groups with just-infinite C*-algebra. This answers a question from [2]. Additionally, we show that residually finite groups of finite exponent are never just-infinite.
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Taxonomy
TopicsAdvanced Operator Algebra Research · Mathematical Analysis and Transform Methods · Advanced Banach Space Theory
