A remarkable family of left-ordered groups: Central extensions of Hecke groups
نویسندگان
چکیده
منابع مشابه
A remarkable family of left-orderable groups: central extensions of Hecke groups
Braid groups are relevant in many branches of Mathematics. In recent years, they have been studied as important examples of left-orderable groups (that is, groups admitting a total order which is invariant by left-multiplication). Historically, the first such order on Bn (for all n ≥ 3) was defined by Dehornoy using pure algebraic (and quite deep) methods [5]. Some years later, an alternative g...
متن کاملNatural Central Extensions of Groups
Given a group G and an integer n ≥ 2 we construct a new group e K(G, n). Although this construction naturally occurs in the context of finding new invariants for complex algebraic surfaces, it is related to the theory of central extensions and the Schur multiplier. A surprising application is that Abelian groups of odd order possess naturally defined covers that can be computed from a given cov...
متن کاملSemiversal Central Extensions of Groups
We generalise the concept of universal central extensions for perfect groups to arbitrary finite groups. This construction, called the semiversal central extension of the group, has the property that it contains every cover of this group as a subquotient.
متن کاملUniversal Locally Finite Central Extensions of Groups
DEFINITION. A group G is called a universal locally finite central extension of A provided that the following conditions are satisfied. (i) A <= (G (the centre of G). (ii) G is locally finite. (iii) (/1-injectivity). Suppose that A <= B <= D with A a (D, that D/A is finite, and that q>: B -> G is an ^-isomorphism (that is, q>{a) = a for all as A). Then there exists an extension q>: D -*• G of (...
متن کاملOn central Frattini extensions of finite groups
An extension of a group A by a group G is thought of here simply as a group H containing A as a normal subgroup with quotient H/A isomorphic to G. It is called a central Frattini extension if A is contained in the intersection of the centre and the Frattini subgroup of H . The result of the paper is that, given a finite abelian A and finite G, there exists a central Frattini extension of A by G...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2011
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2010.10.020