Finite groups whose generalized hypercenter contains certain subgroups of prime power order (original) (raw)

Abstract

In this paper, we investigate the structure of a finite group G under the assumption that certain abelian subgroups of largest possible exponent of prime power order lie in the generalized hypercenter of the group G , and some known results on supersolvability of finite groups are generalized.

Loading...

Loading Preview

Sorry, preview is currently unavailable. You can download the paper by clicking the button above.

References (14)

  1. R.K. Agrawal, Generalized center and hypercenter of a finite group, Proc. Amer. Math. Soc., 54(1976) 13-21.
  2. M. Asaad and M. Ezzat Mohamed, On generalized hyper- center of a finite group, Comm. Algebra, 29(5)(2001) 2239- 2248.
  3. M. Asaad and M.Ezzat Mohamed, Finite groups with quasi- normal subgroups of prime power order, Acta Math. Hungar., 89(4)(2000) 321-326.
  4. M. Asaad, A.A. Heliel and M. Ezzat Mohamed, Finite groups with some S-quasinormally embedded, Comm. Algebra, 32 (5)(2004) 2019-2027.
  5. M. Asaad, M. Ramadan and M.Ezzat, Finite groups with normal subgroups of prime power order, PU. M. A., 5(3) (1994) 251-256.
  6. J. Buckley, Finite groups whose minimal subgroups are normal, Math. Z.,116(1970) 15-17.
  7. B. Huppert, Endiche Gruppen I, Berlin, Springer-Verlag, Berlin, 1979.
  8. O. H. Kegel, Sylow-Gruppen und subnormalteiler endlicher gruppen, Math. Z. 78, (1962) 205-221.
  9. N.P.Mukherjee, The hyperquasicenter of a finite group I, Proc. Amer. Math. Soc., 26(1970) 239-243.
  10. O.Ore, Contributions to the theory of groups of finite order, Duke. Math. J. 5(1939), 431-460.
  11. M. Ramadan, The influence of S-quasinormality of some sub- groups of prime power order on the structure of finite groups, Arch. Math. 77, (2001) 143-148.
  12. M. Ramadan, The influence of certain abelian subgroups on the structure of finite groups, Algebra Colloquium 15:3(2008) 479-484.
  13. P. Schmid, Subgroup permutable with all Sylow subgroups, J. Algebra, 207(1998) 285-293.
  14. M. Weinstein (editor), Between nilpotent and solvable, Polyg onal Publishing House, Passaic, New Jersey, 1982. Received: April, 2012