The generalised Fitting subgroup of a finite group is the group generated by all subnormal subgroups that are either nilpotent or quasisimple. The importance of this subgroup in finite group theory stems from the fact that it always contains its own centraliser, so that any finite group is an abelian extension of a group of automorphisms of its generalised Fitting subgroup. We define a class of...

A nilpotent group G is a finite group that is the direct product of its Sylow p-subgroups. Theorem 1.1 (Fitting's Theorem) Let G be a finite group, and let H and K be two nilpotent normal subgroups of G. Then HK is nilpotent. Hence in any finite group there is a unique maximal normal nilpotent subgroup, and every nilpotent normal subgroup lies inside this; it is called the Fitting subgroup, and...

We exhibit efficient algorithms to perform the following task: Given a function f defined on a finite subset E ⊂ R, compute a C function F on R, with a controlled C norm, that approximates f on the subset E.

in this paper, we extend the construction of a fuzzy subgroup generated by a fuzzy subset to $l$-setting. this construction is illustrated by an example. we also prove that for an $l$-subset of a group, the subgroup generated by its level subset is the level subset of the subgroup generated by that $l$-subset provided the given $l$-subset possesses sup-property.

This work considers the problem of fitting data on a Lie group by a coset of a compact subgroup. This problem can be seen as an extension of the problem of fitting affine subspaces in R to data which can be solved using principal component analysis. We show how the fitting problem can be reduced for biinvariant distances to a generalized mean calculation on an homogeneous space. For biinvariant...