A decomposition theorem for topological group extensions
نویسندگان
چکیده
منابع مشابه
A Lebesgue Decomposition for Elements in a Topological Group
Our aim is to establish the Lebesgue decomposition for strongly-bounded elements in a topological group. In 1963 Richard Darst established a result giving the Lebesgue decomposition of strongly-bounded elements in a normed Abelian group with respect to an algebra of projection operators. Consequently, one can establish the decomposition of strongly-bounded additive functions defined on an algeb...
متن کاملCauchy–davenport Theorem in Group Extensions
Let A and B be nonempty subsets of a finite group G in which the order of the smallest nonzero subgroup is not smaller than d = |A| + |B| − 1. Then at least d different elements of G has a representation in the form ab, where a ∈ A and b ∈ B. This extends a classical theorem of Cauchy and Davenport to noncommutative groups. We also generalize Vosper’s inverse theorem in the same spirit, giving ...
متن کاملA Decomposition Theorem for Cayley Graphs of Picard Group Quotients
The Picard group is defined as Γ = SL(2,Z[i]); the ring of 2× 2 matrices with Gaussian integer entries and determinant one. We consider certain graphs associated to quotients Γ/Γ(p) where p is a prime congruent to three mod four and Γ(p) is the congruence subgroup of level p. We prove a decomposition theorem on the vertices of these graphs, and use this decomposition to derive upper and lower b...
متن کاملSome topological proofs and extensions of Grusko's theorem
Homomorphisms h:F ! * G are studied, where F is a free group and * G is the free product. In Part I, the conditions imposed on the homomorphism h relate to certain commutators in F . The method of proof is to obtain a topological realization of h, interpreting F as the fundamental group of a surface with boundary and * G as the fundamental group of a wedge of complexes. Standard general positio...
متن کاملEdge-decomposition of topological indices
The topological indices, defined as the sum of contributions of all pairs of vertices (among which are the Wiener, Harary, hyper–Wiener indices, degree distance, and many others), are expressed in terms of contributions of edges and pairs of edges.
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: Pacific Journal of Mathematics
سال: 1971
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1971.36.357