On the Erdos-Ko-Rado property of finite groups of order a product of three primes

Modjtaba Ghorbani, Mina Rajabi-Parsa

Abstract


Let G be a subgroup of the symmetric group Sn. Then G has the Erdos-Ko-Rado (EKR) property, if the size of any intersecting subset of G is bounded above by the size of a point stabilizer of G. The aim of this paper is to investigate the EKR and the strict EKR properties of the groups of order pqr, where p, q, r are three prime numbers.


Keywords


Cayley graph, permutation groups, EKR property

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DOI: http://dx.doi.org/10.5614/ejgta.2019.7.1.3

References

B. Ahmadi, Maximum Intersecting Families of Permutations, Ph.D. thesis. University of Regina, Regina, (2013).

B. Ahmadi and K. Meagher, The Erdo ̋s-Ko-Rado property for some permutation groups, Australas. J. Comb. 61 (1) (2015), 23–41.

M. Bardestani and K. Mallahi-Karai, On the Erdo ̋s-Ko-Rado property for finite groups, J. Algebr. Comb. 42 (2015), 111–128.

P.J. Cameron and C.Y. Ku, Intersecting families of permutations, European J. Combin. 24 (2003), 881-890.

P. Erdo ̋s, Chao Ko and R. Rado, Intersection theorems for systems of finite sets, Quart. J. Math. 12 (1961), 313-320.

P. Frankl and M. Deza, The maximum number of permutations with given maximal or minimal distance, J. Combin. Theory Ser. A. 22 (1977), 352-360.

M. Ghorbani and F. Nowroozi-Larki, Automorphism group of groups of order pqr, Journal of Algebraic Structures and Their Applications 1 (2014), 49–56.

M.Ghorbani and M.Rajabi Parsa, On the spectrum of derangement graphs of order a product of three primes, Journal of Algebraic Structures and Their Applications 6 (2019), 81–89.

C. Godsil and K. Meagher, A new proof of the Erdo ̋s-Ko-Rado theorem for intersecting families of permutations, European J. Combin. 30 (2009), 404-414.

H. Huang and Y. Zhao, Degree versions of the Erdo ̋s-Ko-Rado Theorem and Erdo ̋s hypergraph matching conjecture, arXiv:1605.07535v1.

G. James and M. Liebeck, Representation and Characters of Groups, Cambridge University Press. Cambridge, (1993).

B. Larose and C. Malvenuto, Stable sets of maximal size in Kneser-type graphs, European J. Combin. 25 (2004), 657-673.

T.M. Ligget, Extensions of the Erdo ̋s-Ko-Rado theorem and a statistical application, J. Com- bin. Theory Ser. A 23 (1977), 15-21.

K. Meagher and P. Spiga, An Erdo ̋s-Ko-Rado theorem for the derangement graph of PGL(2, q) acting on the projective line, J. Combin. Theory Ser. A. 118 (2011), 532-544.

K. Meagher and P. Spiga, An Erdo ̋s-Ko-Rado-type theorem for PGL3(q), SIAM J. Discrete Math. 28 (2014), 918-941.

H. Holder, Die Gruppen der ordnungen p3, pq, pqr, p4, Math. Ann. XLIII. (1893), 371–410.

M. Jalali-Rad and A.R. Ashrafi, Erdo ̋s-Ko-Rado properties of some finite groups, Sib. Electron. Math. Reports 13 (2016), 1249–1257

J.S. Rose, A Course on Group Theory, Cambridge University Press (1978).

C.Y. Ku and T.W.H. Wong, Intersecting families in the alternating group and direct product of symmetric groups, Electron. J. Combin. 14 (2007), #R25.

J. Wang and S.J. Zhang, An Erdo ̋s-Ko-Rado-type theorem in Coxeter groups, European J. Combin. 29 (2008), 1112–1115.


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