참고문헌
- A. Abdollahi and M. Zarrin, Non-nilpoten graph of a group, Comm. Algebra, 38(12)(2010), 4390-4403. https://doi.org/10.1080/00927870903386460
- F. Barry, D. MacHale and A. N She, Some supersolvability conditions for finite groups, Math. Proc. Royal Irish Acad., 106A(2)(2006), 163-177. https://doi.org/10.1353/mpr.2006.0000
- S. Dixmier, Exposants des quotients des suites centrales descendantes et ascendantes d'un groupe, C. R. Acad. Sci. Paris, 259(1964), 2751-2753.
- S. Franciosi and F. Giovanni, Soluble groups with many nilpotent quotients, Proc. Royal Irish Acad. Sect. A., 89(1989), 43-52.
- J. E. Fulman, M. D. Galloy, G. J. Sherman and J. M. Vanderkam, Counting nilpotent pairs in finite groups, Ars Combin., 54(2000), 161-178.
- R. M. Guralnick and G. R. Robinson, On the commuting probability in finite groups, J. Algebra, 300(2)(2006), 509-528. https://doi.org/10.1016/j.jalgebra.2005.09.044
- R. M. Guralnick and J. S. Wilson, The probability of generating a finite soluble group, Proc. London Math. Soc., 81(3)(2000), 405-427. https://doi.org/10.1112/S0024611500012569
- W. H. Gustafson, What is the probability that two group elements commute?, Amer. Math. Monthly, 80(9)(1973), 1031-1034. https://doi.org/10.1080/00029890.1973.11993437
- R. Heffernan, D. MacHale and A. N She, Restrictions on commutativity ratios in finite groups, Int. J. Group Theory, 3(4)(2014), 1-12.
- S. M. Jafarian Amiri, H. Madadi and H. Rostami, On the probability of generating nilpotent subgroups in a finite group, Bull. Aust. Math. Soc., 93(3)(2016), 447-453. https://doi.org/10.1017/S0004972715001252
- E. Khamseh, M. R. R. Moghaddam and F. G. Russo, Some Restrictions on the Probability of Generating Nilpotent Subgroups, Southeast Asian Bull. Math., 37(4)(2013), 537-545.
- P. Lescot, H. N. Nguyen and Y. Yang, On the commuting probability and supersolvability of finite groups, Monatsh. Math., 174(2014), 567-576. https://doi.org/10.1007/s00605-013-0535-9
- D. H. McLain, Remarks on the upper central series of a group, Proc. Glasgow Math. Assoc., 3(1956), 38-44. https://doi.org/10.1017/S2040618500033414
- D. J. S. Robinson, A course in the theory of groups, Springer-Verlag New York(1996).
- H. Rostami, The Commutativity Degree in the Class of Nonabelian Groups of Same Order, Kyungpook Math. J., 59(2019), 203-207.
- J. Wilson, The probability of generating a nilpotent subgroup of a finite group, Bull. London Math. Soc., 40(2008), 568-580. https://doi.org/10.1112/blms/bdn016