Characterisation of 5-groups having a X11-covering with Core-free Intersection
Pencirian Kumpulan-5 yang Mempunyai Litupan-X11 dengan Persilangan Bebas-teras
DOI:
https://doi.org/10.37134/jsml.vol9.sp.3.2021Keywords:
Covering of a group, maximal irredundant n¬-covering, core-free intersection, 5-groupsAbstract
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.
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