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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Counting group elements of order $ p$ modulo $ p\sp{2}$


Author: Marcel Herzog
Journal: Proc. Amer. Math. Soc. 66 (1977), 247-250
MSC: Primary 20D99
MathSciNet review: 0466316
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Abstract: Let G be a finite group of order divisible by the prime p. It is shown that the number of elements of G of order p is congruent to $ - 1$ modulo $ {p^2}$, unless a Sylow p-subgroup of G is cyclic, generalized quaternion, dihedral or quasidihedral.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0466316-5
PII: S 0002-9939(1977)0466316-5
Keywords: Finite group, element of order p
Article copyright: © Copyright 1977 American Mathematical Society