Minimal length normal forms for some soluble groups

Minimal Length Elements in Some Double Cosets of Coxeter Groups

We study the minimal length elements in some double cosets of Coxeter groups and use them to study Lusztig’s G-stable pieces and the generalization of G-stable pieces introduced by Lu and Yakimov. We also use them to study the minimal length elements in a conjugacy class of a finite Coxeter group and prove a conjecture in [GKP].

On Minimal Length Factorizations of Finite Groups

Minimal Polynomials and Jordan Normal Forms

groups with a given solvable length , and minimal composition length

Let cS(d) denote the minimal composition length of all finite solvable groups with solvable (or derived) length d. We prove that:

Some comments on fuzzy normal forms

—In this paper, we examine and compare de Morgan-, Kleene-, and Boolean-disjunctive and conjunctive normal forms in fuzzy settings. This generalizes papers of Turksen on the subject of Boolean-normal forms.