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Proceedings of the American Mathematical Society

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Not every $ p$-group can be generated by elements of the same order

Authors: E. A. O'Brien, Carlo M. Scoppola and M. R. Vaughan-Lee
Journal: Proc. Amer. Math. Soc. 134 (2006), 3457-3464
MSC (2000): Primary 20D15
Published electronically: June 12, 2006
MathSciNet review: 2240656
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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.

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Additional Information

E. A. O'Brien
Affiliation: Department of Mathematics, University of Auckland, Auckland, New Zealand

Carlo M. Scoppola
Affiliation: Dipartimento di Matematica Pura ed Applicata, Universita di L’Aquila, Coppito 67010, L’Aquila, Italy

M. R. Vaughan-Lee
Affiliation: Christ Church, University of Oxford, OX1 1DP, United Kingdom

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
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.