Characterization of 7-Groups with a C\(_12\)-Covering - Tarmizi, Rawdah Adawiyah; Sulaiman, Hajar (Journal of Informatics and Mathematical Sciences, 2016)
A group G is covered by a collection of its proper subgroups if it is equal to the union of the collection. A covering is called irredundant if it has no proper sub-collection which also covers G. A covering of G in which all members are maximal subgroups is called maximal. For any integer , a covering with n members is called an n-covering. We call the covering of G as Cn–covering if it is an irredundant maximal n-covering with core free intersection for G, and we call a group G a Cn–group if G admits a Cn–covering. In this paper, we completely characterize 7-groups having a maximal irredundant 12-covering with core-free intersection. From our results, it is proven that a group G is a 7-group having C12–covering if and only if .