In a recent paper on study of the Sylow 2-subgroups symmetric group with 2^n elements it has been show that growth first (n-2) consecutive indices certain normalizer chain is linked to sequence partitions integers into distinct parts. Unrefinable parts are those in which no part x can be replaced whose sum obtaining new partition We prove here (n-1)-th index previously mentioned related number ...

in this paper, we study the notion of solvable $l$-subgroup of an $l$-group and provide its level subset characterization and this justifies the suitability of this extension. throughout this work, we have used normality of an $l$-subgroup of an $l$-group in the sense of wu rather than liu.

suppose that $h$ is a subgroup of $g$‎, ‎then $h$ is said to be‎ ‎$s$-permutable in $g$‎, ‎if $h$ permutes with every sylow subgroup of‎ ‎$g$‎. ‎if $hp=ph$ hold for every sylow subgroup $p$ of $g$ with $(|p|‎, ‎|h|)=1$)‎, ‎then $h$ is called an $s$-semipermutable subgroup of $g$‎. ‎in this paper‎, ‎we say that $h$ is partially $s$-embedded in $g$ if‎ ‎$g$ has a normal subgroup $t$ such that $ht...

We describe some new ways to construct saturated fusion subsystems, including, as a special case, the normalizer of set components ambient system. This was motivated in part by Aschbacher's construction one component, and joint work with three other authors where we had all components.

Let X be a non-degenerate left Banach module over a normed algebra A having a bounded approximate left identity. We show that, if A is a left ideal of a larger algebra, then this representation can be extended to a representation of the larger algebra. Based on this result, we study in detail the existence and properties of representations of the various centralizer algebras of A which are comp...

Let g be a real semisimple Lie algebra and θ a fixed Cartan involution of g. In this paper the subscript C is used for indicating the complexification of a real object. Denote the universal enveloping algebra of the complex Lie algebra gC by U(gC), the center of U(gC) by Z(gC), and the symmetric algebra of gC by S (gC). Similar notation is used for other complex Lie algebras or vector spaces. L...