Products of Sylow Subgroups in Suzuki and Ree Groups

Abstract

An explicit and elementary proof is given to the fact that Suzuki and Ree groups can be decomposed into the product of 4 of their Sylow psubgroups, where p is the defining characterictic.

Factorizations of finite groups by conjugate subgroups which are solvable or nilpotent

“…After the completion of our proof of Theorem 1.2, and in parallel to its publication in preprint form ( [18]), Smolensky made available a preprint in which he shows that every Suzuki and Ree group is a product of four unipotent Sylow subgroups ( [30]). Thus, the results in [32], [33], [34], [29] and [30], combine to give a different proof of the four Sylow claim of Theorem 1.2. Theorem 1.2 and the cp-factorization of finite simple groups of Lie type by Borel subgroups mentioned above clearly motivate a general study of cp-factorizations of a finite group G by subgroups which are nilpotent or solvable.…”

Minimal length factorizations of finite simple groups of Lie type by unipotent Sylow subgroups

“…After the completion of our work, and in parallel to its publication in preprint form [6], Smolensky made available a preprint in which he shows that every Suzuki and Ree group is a product of four unipotent Sylow subgroups [12]. Thus, the results in [14], [15], [16], [13], [11] and [12], combine to give a different proof of the four Sylow claim of Theorem 1.…”

“…Thus, the results in [14], [15], [16], [13], [11] and [12], combine to give a different proof of the four Sylow claim of Theorem 1.…”