Characterization of 7-Groups with a C\(_{12}\)-Covering

Authors

  • Rawdah Adawiyah Tarmizi School of Mathematical Sciences, Universiti Sains Malaysia
  • Hajar Sulaiman School of Mathematical Sciences, Universiti Sains Malaysia

DOI:

https://doi.org/10.26713/jims.v8i4.562

Keywords:

covering groups by subgroups, p-groups, maximal irredundant covering, core-free intersection

Abstract

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 .

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References

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Published

2016-12-31
CITATION

How to Cite

Tarmizi, R. A., & Sulaiman, H. (2016). Characterization of 7-Groups with a C\(_{12}\)-Covering. Journal of Informatics and Mathematical Sciences, 8(4), 267–272. https://doi.org/10.26713/jims.v8i4.562

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Section

Research Articles