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Research Articles

Lengths of conjugacy classes of π-elements and primary elements in finite groups

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Pages 2947-2955 | Received 07 Nov 2021, Accepted 16 Jan 2023, Published online: 11 Feb 2023

References

  • Beidleman, J. C., Robinson, D. J. S. (1997). On finite groups satisfying the permutizer condition. J. Algebra 191:686–703. DOI: 10.1006/jabr.1996.6932.
  • Beltrán, A., Felipe, M. J. (2007). Nilpotency of p-complements and p-regular conjugacy class sizes. J. Algebra 308:641–653. DOI: 10.1016/j.jalgebra.2006.10.007.
  • Camina, A. R., Camina, R. D. (1998). Implications of conjugacy class size. J. Group Theory 1(3):257–269.
  • Camina, A. R., Camina, R. D. (2011). The influence of conjugacy class sizes on the structure of finite groups: a survey. Asian-Eur. J. Math., 4:559–588. DOI: 10.1142/S1793557111000459.
  • Chen, C. (1988). Inner and Outer Σ-Groups and Minimal non Σ-Groups. Chongqing: Northwest Normal University (in Chinese).
  • Chillag, D., Herzog, M. (1990). On the length of the conjugacy classes of finite groups. J. Algebra 131::110–125. DOI: 10.1016/0021-8693(90)90168-N.
  • Cossey, J., Wang, Y. (1999). Remarks on the length of conjugacy classes of finite groups. Commun. Algebra 27(9):4347–4353. DOI: 10.1080/00927879908826701.
  • Fein, B., Kantor, W. M., Schacher, M. (1981). Relative Brauer groups II. J. Reine Angew Math. 328:39–57.
  • Felipe, M. J., Martínez-Pastor, A., Ortiz-Sotomayor, V. M. (2017). Square-free class sizes in products of groups. J. Algebra 491:190–206. DOI: 10.1016/j.jalgebra.2017.08.007.
  • Gluck, D., Wolf, T. R. (1984). Brauer’s height conjecture for p-solvable groups. Trans. Amer. Math. Soc. 282(1): 137–152.
  • Gluck, D. (1983). Trivial set-stabilizers in finite permutation groups. Can. J. Math. 35(1):59–67.
  • Gorenstein, D. (1980). Finite Groups, 2nd. New York: Chelsea Publishing Company.
  • Guo, X., Zhao, X., Shum, K. P. (2009). On p-regular G-conjugacy classes and the p-structure of normal subgroups. Commun. Algebra 37(6):2052–2059. DOI: 10.1080/00927870802304689.
  • Huppert, B. (1967). Endliche Gruppen I. Berlin: Springer Verlag.
  • Isaacs, I. M. (1976). Character Theory of Finite Groups. New York: Academic Press.
  • Isaacs, I. M. (1986). Solvable groups character degrees and sets of primes. J. Algebra 104:209–219. DOI: 10.1016/0021-8693(86)90211-5.
  • Kong, Q. (2018). Conjugacy class sizes of elements of prime-power order of finite groups. Bull. Iran. Math. Soc. 44:405–408. DOI: 10.1007/s41980-018-0026-9.
  • Liu, X. (2010). Notes on the length of conjugacy classes of finite group II. Sci. China Math. 40(6):539–544 (in Chinese).
  • Qian, G., Wang, Y. (2014). On conjugacy class sizes and character degrees of finite groups. J. Algebra Appl. 13(2):1350100-1-9. DOI: 10.1142/S0219498813501004.
  • Ren, Y. (1994). The length of conjugacy classes and the structure of finite groups. Adv. Math. 23(5):405–410 (in Chinese).
  • Shao, C., Jiang, Q. (2020). Determining group structure by set of conjugacy class sizes. Commun. Algebra 48(4):1626–1631. DOI: 10.1080/00927872.2019.1691580.

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