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Secretive prime-power groups of large rank

Published online by Cambridge University Press:  17 April 2009

G.E. Wall
G.E. Wall
Affiliation:
Department of Pure Mathematics, University of Sydney, Sydney, New South Wales.
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Abstract

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A question of L.G. Kovács, Joachim Neubüser, B.H. Neumann (J. Austral. Math. Soc. 12 (1971), 287–300) on the existence of ‘secretive’ prime-power groups of large rank is settled affirmatively by proving the following result: given a prime p and integer d ≥ 2, there exists a finite p–group P with cyclic centre and minimal number of generators d and having the property that every element not in its Frattini subgroup has a non-trivial power in its centre.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 12 , Issue 3 , June 1975 , pp. 363 - 369
Copyright
Copyright © Australian Mathematical Society 1975

References

[1]Chevalley, C., “Démonstration d'une hypothèse de M. Artin”, Abh. Math. Sem. Univ. Hamburg 11 (1936), 73–75.CrossRefGoogle Scholar
[2]Kovács, L.G., Neubüser, Joachim, Neumann, B.H., “On finite groups with ‘hidden’ primes”, J. Austral. Math. Soo. 12 (1971), 287–300.CrossRefGoogle Scholar