MULTI VAGUE ORDER OF AN ELEMENT IN A GROUP

Abstract

In this paper, we introduce the concept of Multi vague
order of an element in a group with dimension k which
extends the classical notion of vague order. We establish
various properties and characterizations of Multi vague groups
based on this order.
Further, we study the concepts of Multi vague-p group,
Multi vague torsion. For instance, we show that GVA =
{x ∈ G | tiA(x) = tiA(e) & fiA(x) = fiA(e), i = 1, 2, ...., k.}
is a normal subgroup of G, and that A is a Multi vague-p
International Journal of Applied Mathematics
group if and only if the quotient group G
GVA
is a p-group.
Moreover, if A is a Multi vague group of an abelian group
G, then A is Multi vague torsion if and only if G
GVA
is a
torsion group.