Review of a Trilogy about Sylow Theory in Locally Finite Groups (Contemporary Mathematics, 2023)
This comprehensive review concerns the trilogy about Sylow Theory in Locally Finite Groups which has been published in four books by Books on Demand (BoD), Norderstedt, Germany, namely: Part 1 - ISBN 978-3-7543-6087-3 (November 2022); Part 1 - Second edition - ISBN 978-3-7568-0801-4 (March 2023); Part 2 - ISBN 978-3-7568-3892-9 (December 2022); Part 3 - ISBN 978-3-7568-9853-4 (January 2023).
Keywords: locally finite group satisfying the Strong Sylow Theorem for the prime p (or the Strong Sylow p-Theorem); singular (Sylow) p-subgroup; (very) good Sylow p-subgroup; p-uniqueness subgroup; minimal (w.r.t. order) p-unique subgroup; (numerical) Sylow p-invariant ap; simple group; nested local system; amily T of types of known finite simple groups; simple locally finite group of type Ξ∈T; rank of a locally finite simple group; P-invariant Sylow p-subgroup; Kegel cover; Kegel sequence; conjugacy class; P-isomorphic P-orbit; p-length of a p-soluble finite group; Hall-Higman Theory; locally finite field F; algebraic closure of the prime field in characteristic p; General Linear Group; Special Linear Group; Projective Special Linear (PSL) Group; G-module over a (locally finite) field F; irreducibility; complete reducibility; non-modular G-module; modular G-module; G-isomorphic G-modules; Jordan normal form; Classical Group; group of Lie type; twisted Chevalley group