Proceedings of the Japan Academy, Series A, Mathematical Sciences

``Hasse principle'' for extraspecial $p$-groups

Manoj Kumar and Lekh Raj Vermani

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Abstract

A group $G$ is said to enjoy ``Hasse principle'' if every local coboundary of $G$ is a global coboundary. It is proved that every non-Abelian finite $p$-group having a miximal subgroup which is cyclic and every extraspecial $p$-group enjoy ``Hasse principle''.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 76, Number 8 (2000), 123-125.

Dates
First available in Project Euclid: 23 May 2006

Permanent link to this document
https://projecteuclid.org/euclid.pja/1148393455

Digital Object Identifier
doi:10.3792/pjaa.76.123

Mathematical Reviews number (MathSciNet)
MR1794568

Zentralblatt MATH identifier
0995.20034

Subjects
Primary: 20D15: Nilpotent groups, $p$-groups 20D40: Products of subgroups

Keywords
Cocycle coboundary Hasse principle central product extraspecial $p$-groups

Citation

Kumar, Manoj; Vermani, Lekh Raj. ``Hasse principle'' for extraspecial $p$-groups. Proc. Japan Acad. Ser. A Math. Sci. 76 (2000), no. 8, 123--125. doi:10.3792/pjaa.76.123. https://projecteuclid.org/euclid.pja/1148393455


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References

  • Gaschütz, W.: Kohomogische Trivialitäten und äussere Automorphismen von $p$-gruppen. Math. Z., 88, 432–433 (1965).
  • Gaschütz, W.: Nichtabelsche $p$-Gruppen besitzen äussere $p$-Automorphismen. J. Algebra, 4, 1–2 (1966).
  • Ono, T.: “Shafarevich-Tate sets” for profinite groups. Proc. Japan Acad., 75A, 96–97 (1999).
  • Ono, T., and Wada, H.: “Hasse principle” for free groups. Proc. Japan Acad., 75A, 1–2 (1999).
  • Ono, T., and Wada, H.: “Hasse principle” for symmetric and alternating groups. Proc. Japan Acad., 75A, 61–62 (1999).
  • Suzuki, M.: Group Theory I. Springer, New York-Berlin-Heidelberg-Tokyo (1982).
  • Suzuki, M.: Group Theory II. Springer, New York-Berlin-Heidelberg-Tokyo (1986).