The aim of this research is to contribute further results on the coverings of some finite groups. Only non-cyclic groups are considered in the study of group coverings. Since no group can be covered by only two of its proper subgroups, a covering should consist of at least 3 of its proper subgroups. If a covering contains n (proper) sub- groups, then the set of these subgroups is called an n-covering. The covering of a group G is called minimal if it consists of the least number of proper subgroups among all coverings for the group; i.e. if the minimal covering consists of m proper subgroups then the notation used is σ (G) = m. A covering of a group is called irredundant if no proper subset of the covering also covers the group. Obviously, every minimal cover- ing is irredundant but the converse is not true in general. If the members of the covering are all maximal normal subgroups of a group G, then the covering is called a maximal covering. Let D be the intersection of all members i.....

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Andaikan G adalah kumpulan terhingga. Jika terdapat suatu set yang mengandungi n subkumpulan wajar dalam G yang kesatuannya merangkumi semua unsur bagi G, maka G merupakan kumpulan terlitup. Set bagi n subkumpulan wajar dipanggil litupan-n bagi G dan bilangan minimum bagi n yang melitupi G ialah 3, ini bermakna n X 3 . Jika litupan-n tidak mempunyai subset wajar yang juga melitupi G, maka ia dipanggil litupann tak berlebihan bagi G dan ia dipanggil litupan-n maksimal jika ia mengandungi hanya subkumpulan maksimal bagi G. Suatu litupan-n tak berlebihan maksimal dengan persilangan bebas-teras dikenali sebagai suatu litupan-Xn. Kajian ini mencirikan kumpulan-5 yang mempunyai suatu litupan-X11. Didapati bahawa kumpulan-5 mempunyai litupan-X11 jika dan hanya jika ia berisomorfisma dengan beberapan kumpulan abelan bagi sesetengah peringkat.  ..

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