Not every $p$-group can be generated by elements of the same order
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- by E. A. O’Brien, Carlo M. Scoppola and M. R. Vaughan-Lee PDF
- Proc. Amer. Math. Soc. 134 (2006), 3457-3464 Request permission
Abstract:
For every prime $p$, we exhibit a finite $p$-group which cannot be generated by a set of elements, all having the same order. This answers a long-standing question from the Kourovka Notebook.References
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Additional Information
- E. A. O’Brien
- Affiliation: Department of Mathematics, University of Auckland, Auckland, New Zealand
- MR Author ID: 251889
- Email: obrien@math.auckland.ac.nz
- Carlo M. Scoppola
- Affiliation: Dipartimento di Matematica Pura ed Applicata, Universita di L’Aquila, Coppito 67010, L’Aquila, Italy
- Email: scoppola@univaq.it
- M. R. Vaughan-Lee
- Affiliation: Christ Church, University of Oxford, OX1 1DP, United Kingdom
- Email: michael.vaughan-lee@christ-church.oxford.ac.uk
- Received by editor(s): July 6, 2005
- Published electronically: June 12, 2006
- Additional Notes: The first author was supported by GNSAGA-INdAM and by EPSRC grant GR/S86259/01 while this paper was written
The second author is a member of GNSAGA-INdAM - Communicated by: Jonathan I. Hall
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 134 (2006), 3457-3464
- MSC (2000): Primary 20D15
- DOI: https://doi.org/10.1090/S0002-9939-06-08576-5
- MathSciNet review: 2240656