EAN: 9783959355940

ON THE STRUCTURE OF THE SOLOMON-TITS ALGEBRA OF...

Within this work we study the structure of the Solomon-Tits algebra of the symmetric group
motivated by results of research done by Manfred Schocker about the module structure of this
algebra. We investigate three structures: the associative  the associated Lie algebra and the
group of units. All three structures are related and can be studied in the more general context
of associative soluble splittable algebras possessing a self-centralizing radical complement.
Our results are related to dimension formulas  Duo algebras  self-centralization of the radical
complements  Cartan subalgebras  Sylow subgroups  Hall subgroups  Carter subgroups  stagnation
of central chains  classes of nilpotency and solvability  exponents alongside central chains 
nilradical and Fitting subgroup  semisimple and simple substructures  anti-automoprhism and
irreducible character values.

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