Pencirian Kumpulan-5 yang Mempunyai Litupan-X11 dengan Persilangan Bebas-teras

Abstract

Let G be a finite group. If there is a set containing n proper subgroups in G whose union comprises all elements of G, then G is a coverable group. The set of n proper subgroups is called an n-covering for G and the minimum number of n covers G is 3, so this means. If the n-covering has no proper subset that also covers G then it is called an irredundant n-covering for G and it is called a maximal n-covering if it consists of only maximal subgroups. A maximal irredundant n-covering with a core-free intersection is known as a Cn-covering. This study characterizes 5-groups having a C11-covering. It was found that a 5-group has a C11-covering if and only if it is isomorphic to some elementary abelian groups of a certain order.