In this paper we prove that for every n >= 3, there exists a permutation 3-group P-n, such that P-n, has five orbits, each of size at least 3(2n-1), and P-n, has no fixed-point-free element. In particular, this gives, for the prime 3, an answer to a conjecture in [2] and [4]
Spiga, P. (2013). Permutation 3-groups with no fixed-point-free elements. ALGEBRA COLLOQUIUM, 20(3), 383-394 [10.1142/S1005386713000357].
Permutation 3-groups with no fixed-point-free elements
SPIGA, PABLO
2013
Abstract
In this paper we prove that for every n >= 3, there exists a permutation 3-group P-n, such that P-n, has five orbits, each of size at least 3(2n-1), and P-n, has no fixed-point-free element. In particular, this gives, for the prime 3, an answer to a conjecture in [2] and [4]
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