Bondarenko N. Lie algebras associated with Sylow p-subgroups of finite symmetric groups

Thesis is devoted to study of Lie algebras associated with Sylow p-subgroups of symmetric groups of degree p^m, m є N. The tableau representation Lm of such Lie algebras is constructed. The lower and the upper central series, the commutant series and the engel series are described. The notion of the wreath product of arbitrary Lie algebra with an abelian finite-dimensional Lie algebra over the prime field Fp of the characteristic p is introduced. It is proved that the Lie algebra Lm is isomorphic to the m-iterated wreath product of one-dimensional Lie algebras over the field Fp. It is shown that the Lie algebra Lm can be embedded to the Lie algebra of the upper 0-triangular matrices of the order p^(m-1)+1 over the field Fp and the Lie algebra of the upper 0-triangular matrices of the order m over the field Fp can be embedded to the Lie algebra L(m-1).