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 .

Downloads

Download data is not yet available.

References

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

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

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

A. Abdollahi and S. J. Amiri, On groups with an irredundant 7-cover, Journal of pure and applied algebra, 209(2) (2007), 291-300.

A. Blokhuis, Note on the size of a blocking set in PG(2, p), Combinatorica 14(1) (1994), 111-114.

C. A. Baker and L.M. Batten, Finite Geometries, Marcel Dekker Inc, New York, (1985).

D. Greco, Sui gruppichesonosomma di quattro o cinquesottogruppi.Rend, Accad.delleScienze di Napoli (4) 23(1956), 49-56.

G. Scorza, gruppichepossonopensarsi come somma di trelorosottogruppi, Boll. Un. Mat. Ital 5 (1926), 216-218.

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

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

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

U. Heim, Proper blocking sets in projective spaces, Discrete Math 174 (1997), 167-176.

The GAP Group, GAP – Groups, Algorithms, and Programming, Version 4.3 (2002), http://www.gap-system.org.

Downloads

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

Issue

Vol. 8 No. 4 (2016)

Section

Research Articles

License

Authors who publish with this journal agree to the following terms:
  • Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a CCAL that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  • Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  • Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.