# Characterisation of 5-groups having a X11-covering with Core-free Intersection

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

• Rawdah Adawiyah Tarmizi Jabatan Matematik, Fakulti Sains dan Matematik, Universiti Pendidikan Sultan Idris, Tanjong Malim, Perak, Malaysia
• Hajar Sulaiman Pusat Pengajian Sains Matematik, Universiti Sains Malaysia, USM, Penang, Malaysia
Keywords: Covering of a group, maximal irredundant n¬-covering, core-free intersection, 5-groups

### 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.

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Published
2021-02-18
How to Cite
Tarmizi, R. A., & Sulaiman, H. (2021). Characterisation of 5-groups having a X11-covering with Core-free Intersection. Journal of Science and Mathematics Letters, 9, 18-27. https://doi.org/10.37134/jsml.vol9.sp.3.2021
Section
Articles