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Groups in which the hypercentral factor group is a T-group

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Abstract

We consider groups G having a T - group as factor G/Z*(G) and exhibit connections with its Frattini subgroup and its nilpotemt radical.Mutually permutable products of these groups with supersolvable ones are described with consequences concerning the Fitting core of supesolvable groups.

Keywords: Hypercenter, T-group, Fitting core

Mathematics Subject Classification (2000): 20D25, 20D40, 20D10

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References

  • 1. Agrawal, R.K.: Finite groups whose subnormal subgroups permute with all Sylow subgroups. Proc. Amer. Math. Soc. 47, 77–83 (1975)

    Google Scholar 

  • 2. Alejandre, M.J., Ballester-Bolinches, A., Cossey, J.: Permutable products of supersolvable groups. J. Algebra 276, 453–461 (2004)

    Google Scholar 

  • 3. Asaad, M., Shaalan, A: On the supersolvability of finite groups. Arch. Math.(Basel) 53, 318–326 (2004)

    Google Scholar 

  • 4. Ballester-Bolinches, A., Cossey, J., Pedraza-Aguilera, M.C.: On mutually permutable products of finite groups. J. Algebra 294, 127–135 (2005)

    Google Scholar 

  • 5. Ballester-Bolinches, A., Esteban-Romero, R., Pedraza-Aguilera, M.C.: On a class of p-soluble groups. Algebra Colloquium 12, 263–267 (2005)

    Google Scholar 

  • 6. Beidleman, J.C., Heineken, H.: On the Fitting core of a formation. Bull. Australian Math. Soc. 68, 107–112 (2003)

    Google Scholar 

  • 7. Beidleman, J.C., Heineken, H.: Mutually permutable subgroups and group classes. Arch. Math.(Basel) 85, 18–30 (2005)

    Google Scholar 

  • 8. Beidleman, J.C., Heineken, H.: Group classes and mutually permutable products. J. Algebra 297, 409–416 (2006)

    Google Scholar 

  • 9. Beidleman, J.C., Heineken, H.: Finite souble groups whose subnormal subgroups permute with certain classes of subgroups. J. Group Theory 6, 139–158 (2003)

    Google Scholar 

  • 10. Gaschütz, W.: Gruppen, in denen das Normalteilersein transitiv ist. J. Reine u. Angew. Math. 198, 87–92 (1957)

    Google Scholar 

  • 11. Van der Wall, R.W., Fransman, A.: On products of groups for which normality is a transitive relation on their Frattini factor groups. Quaestiones Math. 19, 59–82 (1996)

    Google Scholar 

Download references

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Authors and Affiliations

  1. Department of mathematics, University of Kentucky, Lexington, Kentucky 40506-0027, U.S.A.

    James C. Beidleman

  2. Mathematisches Institut, Universität Würzburg, Am Hubland, 97074 Würzburg, Germany

    Hermann Heineken

Authors
  1. James C. Beidleman
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  2. Hermann Heineken
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Beidleman, J.C., Heineken, H. Groups in which the hypercentral factor group is a T-group. Ricerche mat. 55, 59–65 (2006). https://doi.org/10.1007/s11587-006-0012-z

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  • DOI: https://doi.org/10.1007/s11587-006-0012-z

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