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


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.


Download data is not yet available.


Abdollahi, A. (2009). Groups with maximal irredundant covers and minimal blocking sets. arXiv preprint arXiv.0901.1793.

Abdollahi, A., Ataei, J., & Hassanabadi, M. (2005). Groups with a maximal irredundant 6-cover. Communications in Algebra, 33(9), 3225–3238.

Abdollahi, A., Ataei, J., & Hassanabadi, M. (2008). Minimal blocking sets in PG(n,2) and covering groups by subgroups. Communications in Algebra, 36(2), 365–380.

Abdollahi, A., & Jafarian, A. S. (2008). On groups with an irredundant 7-cover. Journal of pure and applied algebra, 209(2), 291–300.

Ataei, M. J. (2010). C8-groups and nilpotency condition. International Journal of Algebra, 4(22), 1057–1062.

Ataei, M. J., & Sajjad, V. (2011). Characterization of 5-groups with a maximal irredundant 10-cover. International Mathematical Forum, 35(6), 1733–1738.

Bryce, R. A., Fedri, V., & Serena, L. (1997). Covering groups with subgroups. Bulletin of the Australian Mathematical Society, 55(3), 469–476.

Greco, D. (1953). Su alcunigruppifinitichesonosomma di cinquesottogruppi. Rend. Sem. Mat. Univ. Padova: 22, 313–333.

Hungerford, T. W. (1974). Algebra. New York, NY: Springer.

Newton, B. (2011). On the number of maximal subgroups of a finite solvable group. Archiv der Mathematik, 96(6): 501–506.

Tarmizi, R. A., & Sulaiman, H. (2016). Characterization of 7-Groups with a C12-Covering. Journal of Informatics and Mathematical Sciences, 8(4), 267-272.

Abd Manaf, F. N., Sarmin, N. H., Mohd Ali, N. M., & Erfanian, A. (2019). On The Exterior Degree of Some Finite p-Groups. Journal of Science and Mathematics Letters, 4(2), 69-74. Retrieved from

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.