Skip to main content
Log in

A classification of some regular p-groups and its applications

  • Published:
Science in China Series A Aims and scope Submit manuscript

Abstract

In this paper we classify regular p-groups with type invariants (e/it, 1, 1, 1) for e⩾2 and (1, 1, 1, 1, 1). As a by-product, we give a new approach to the classification of groups of order p 5, p⩾5 a prime.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Hall, P., A contribution to the theory of groups of prime-power order, Proc. London Math. Soc., 1934, 36: 29–95.

    Google Scholar 

  2. Xu, M. Y., P. Hall’s basis theorem for regular p-groups and its application to some classification problems, Communications in Algebra, 1991, 19: 1271–1280.

    MATH  MathSciNet  Google Scholar 

  3. James, R. K., The groups of order p 6 (p an odd prime), Math. Comp., 1980, 34: 614–637.

    Google Scholar 

  4. Newman, M. F., O’Brien, E. A., Vaughan-Lee, M. R., Groups and nilpotent Lie rings whose order is the sixth power of a prime, J. Algebra, 2004, 278: 383–401.

    Article  MathSciNet  Google Scholar 

  5. Bagnera, G., La composizione dei Gruppi finiti il cui grado é la quinta potenza mid un numero primo, Ann. Mat. Pura. Appl., 1898, 1(3): 137–228.

    MATH  Google Scholar 

  6. Bender, H. A., A determination of the groups of order p 5, Ann. Math., 1927, 29(2): 61–72.

    MATH  MathSciNet  Google Scholar 

  7. De Séguier, J. A., Théorie des groupes finis. Éléments de la théorie des groupes abstraits, Paris: Gauthier-Villars, 1904.

    Google Scholar 

  8. Schreier, O., Über die Erweiterung von Gruppen II, Abh. Math. Sem. Univ. Hamburg, 1926, 4: 321–346.

    MATH  Google Scholar 

  9. Huppert, B., Über das Produkt von paarweise vertauschbaren zyklischen Gruppen, Math. Z., 1953, 58: 243–264.

    Article  MATH  MathSciNet  Google Scholar 

  10. Newman, M. F., Xu, M. Y., Metacyclic groups of prime-power order (Research announcement), Adv. in Math., 1988, 17: 106–107.

    Google Scholar 

  11. Xu, M. Y., A theorem on metabelian p-groups and some consequences, Chin. Ann. Math., 1984, 5B: 1–6.

    Google Scholar 

  12. Ji, Y. H., Du, S. F., Zhang, L. L., A classification of regular p-groups with invariants (e, 2, 1), Southeast Asian Bull. Math., 2001, 25: 245–256.

    MathSciNet  Google Scholar 

  13. Wilkinson, D., The groups of exponent p and order p 7 (p any prime), J. Algebra, 1988, 118: 109–119.

    Article  MATH  MathSciNet  Google Scholar 

  14. Huppert, B., Endliche Gruppen I, Berlin: Springer-Verlag, 1967.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to Zhang Qinhai or Xu Mingyao.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhang, Q., Song, Q. & Xu, M. A classification of some regular p-groups and its applications. SCI CHINA SER A 49, 366–386 (2006). https://doi.org/10.1007/s11425-006-0366-4

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11425-006-0366-4

Keywords

Navigation