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CLT-Groups with Hall S-Quasinormally Embedded Subgroups

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Ukrainian Mathematical Journal Aims and scope

A subgroup H of a finite group G is said to be Hall S-quasinormally embedded in G if H is a Hall subgroup of the S-quasinormal closure H SQG . We study finite groups G containing a Hall S-quasinormally embedded subgroup of index p n for each prime power divisor p n of the order of G.

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References

  1. A. Ballester-Bolinches, J. C. Beidleman, and R. Esteban-Romero, “On some classes of supersoluble groups,” J. Algebra, 312, 445–454 (2007).

    Article  MATH  MathSciNet  Google Scholar 

  2. A. Ballester-Bolinches, R. Esteban-Romero, and M. Asaad, Products of Finite Groups,Walter de Gruyter, Berlin; New York (2010).

    Book  MATH  Google Scholar 

  3. F. Barry, “The commutator subgroup and CLT(NCLT) groups,” Math. Proc. R. Ir. Acad. A, 104, 119–126 (2004).

    Article  MathSciNet  Google Scholar 

  4. F. Barry, D. MacHale, and Á. Ní Shé, “Some supersolvability conditions for finite groups,” Math. Proc. R. Ir. Acad. A, 106, 163–177 (2006).

    Article  Google Scholar 

  5. S. Baskaran, “On product of two CLT normal subgroups,” Math. Nachr., 83, 89–91 (1978).

    Article  MATH  MathSciNet  Google Scholar 

  6. T. R. Berger, “A converse to Lagrange’s theorem,” J. Austral. Math. Soc., 25, 291–313 (1978).

    Article  MATH  Google Scholar 

  7. R. Brandl, “CLT groups and wreath products,” J. Austral. Math. Soc. Ser. A, 42, 183–195 (1987).

    Article  MATH  MathSciNet  Google Scholar 

  8. R. Brandl and P. A. Linnell, “Character degrees and CLT-groups,” Bull. Austral. Math. Soc., 39, 249–254 (1989).

    Article  MATH  MathSciNet  Google Scholar 

  9. H. G. Bray, “A note on CLT groups,” Pacif. J. Math., 27, 229–231 (1968).

    Article  MATH  MathSciNet  Google Scholar 

  10. M. Brennan, “A note on the converse to Lagrange’s theorem,” Math. Gazette, 82, 286–288 (1998).

    Article  MathSciNet  Google Scholar 

  11. M. J. Curran, “Non-CLT groups of small order,” Comm. Algebra, 11, 111–126 (1983).

    Article  MATH  MathSciNet  Google Scholar 

  12. K. Doerk and T. Hawkes, Finite Soluble Groups, Walter de Gruyter, Berlin; New York (1992).

    Book  MATH  Google Scholar 

  13. T. M. Gagen, “A note on groups with the inverse Lagrange property,” Group Theory (Proc. Miniconf., Austral. Nat. Univ., Canberra, 1975): Lect. Notes Math., Springer, Berlin, 573, 51–52 (1977).

  14. H. Heineken, “Groups with all quotient groups Lagrangian,” Arch. Math., 64, 97–102 (1995).

    Article  MATH  MathSciNet  Google Scholar 

  15. C. V. Holmes, “A characterization of finite nilpotent groups,” Amer. Math. Monthly, 73, 1113–1114 (1966).

    Article  MATH  Google Scholar 

  16. J. F. Humphreys, “On groups satisfying the converse of Lagrange’s theorem,” Proc. Cambridge Phil. Soc., 75, 25–32 (1974).

    Article  MATH  MathSciNet  Google Scholar 

  17. J. F. Humphreys and D. L. Johnson, “On Lagrangian groups,” Trans. Amer. Math. Soc., 180, 291–300 (1973).

    Article  MATH  MathSciNet  Google Scholar 

  18. B. Huppert, Endliche Gruppen I, Springer-Verlag, Berlin, etc. (1967).

    Book  MATH  Google Scholar 

  19. N. Jing, “The order of groups satisfying a converse to Lagrange’s theorem,” Mathematika, 47, 197–204 (2000).

    Article  MATH  MathSciNet  Google Scholar 

  20. S. R. Li, J. He, G. P. Nong, and L. Q. Zhou, “On Hall normally embedded subgroups of finite groups,” Comm. Algebra, 37, No. 9, 3360–3367 (2009).

    Article  MATH  MathSciNet  Google Scholar 

  21. J. J. Liu, S. R. Li, and J. He, “CLT-groups with normal or abnormal subgroups,” J. Algebra, 362, 99–106 (2012).

    Article  MATH  MathSciNet  Google Scholar 

  22. D. McCarthy, “Sylow’s theorem is a sharp partial converse to Lagrange’s theorem,” Math. Z., 113, 383–384 (1970).

    Article  MATH  MathSciNet  Google Scholar 

  23. D. H. McLain, “The existence of subgroups of given order in finite groups,” Proc. Cambridge Phil. Soc., 53, 278–285 (1957).

    Article  MATH  MathSciNet  Google Scholar 

  24. O. Ore, “Contributions to the theory of groups of finite order,” Duke Math. J., 5, 431–460 (1939).

    Article  MathSciNet  Google Scholar 

  25. D. J. S. Robinson, A Course in the Theory of Groups, Springer, New York (1982).

    Book  MATH  Google Scholar 

  26. J. N. Salunke and A. R. Gotmare, “Converse of Lagrange’s theorem and solvable groups,” Bull. Marathwada Math. Soc., 10, 36–42 (2009).

    Google Scholar 

  27. R. R. Struik, “Partial converses to Lagrange’s theorem,” Comm. Algebra, 6, 421–482 (1978).

    Article  MATH  MathSciNet  Google Scholar 

  28. R. R. Struik, “Partial converses to Lagrange’s theorem II,” Comm. Algebra, 9, 1–22 (1981).

    Article  MATH  MathSciNet  Google Scholar 

  29. Between Nilpotent and Solvable, M. Weinstein (ed.), Polygonal Publ. House, Passaic, Jersey (1982).

  30. G. Zappa, “Remark on a recent paper of O. Ore,” Duke Math. J., 6, 511–512 (1940).

    Article  MathSciNet  Google Scholar 

  31. L. W. Zhang, “The supersolvability of QCLT groups,” Acta Math. Sinica (N. S.), 1, 378–381 (1985).

    Article  MATH  MathSciNet  Google Scholar 

Download references

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Authors and Affiliations

  1. School of Mathematics and Statistics, Southwest University, Beibei, Chongqing, China

    Jianjun Liu

  2. Guangxi University, Nanning, Guangxi, China

    Shirong Li

Authors
  1. Jianjun Liu
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  2. Shirong Li
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 66, No. 8, pp. 1146–1152, August,

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Liu, J., Li, S. CLT-Groups with Hall S-Quasinormally Embedded Subgroups. Ukr Math J 66, 1281–1288 (2015). https://doi.org/10.1007/s11253-015-1008-1

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  • DOI: https://doi.org/10.1007/s11253-015-1008-1

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