منابع مشابه
Perpendicularity in an Abelian Group
We give a set of axioms to establish a perpendicularity relation in anAbelian group and then study the existence of perpendicularities in (Z n , +) and (Q + , ⋅) and in certain other groups. Our approach provides a justification for the use of the symbol⊥ denoting relative primeness in number theory and extends the domain of this convention to some degree. Related to that, we also consider para...
متن کاملSplitting the Automorphism Group of an Abelian P-group
Let G be an abelian p-group sum of finite homocyclic groups Gi. Here, we determine in which cases the automorphism group of G splits over kerσ, where σ :Aut(G) → ∏ iAut(Gi/pGi) is the natural epimorphism. 1. Preliminaries Throghout this paper, p is an arbitrary prime and r is a fixed ordinal number. Let G = ⊕i≤rGi be an abelian p-group, such that Gi is an homocyclic group of exponent pi and fin...
متن کاملFuzzy Subgroups of Rank Two Abelian p-Group
In this paper we enumerate fuzzy subgroups, up to a natural equivalence, of some finite abelian p-groups of rank two where p is any prime number. After obtaining the number of maximal chains of subgroups, we count fuzzy subgroups using inductive arguments. The number of such fuzzy subgroups forms a polynomial in p with pleasing combinatorial coefficients. By exploiting the order, we label the s...
متن کاملGeneralized Quadrangles with an Abelian Singer Group
In this note we characterize thick finite generalized quadrangles constructed from a generalized hyperoval as those admitting an abelian Singer group, i.e., an abelian group acting regularly on the points.
متن کاملFreiman’s Theorem in an Arbitrary Abelian Group
A famous result of Freiman describes the structure of finite sets A ⊆ Z with small doubling property. If |A + A| 6 K|A| then A is contained within a multidimensional arithmetic progression of dimension d(K) and size f(K)|A|. Here we prove an analogous statement valid for subsets of an arbitrary abelian group.
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: 2009
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2008.12.021