Abstract
Let π be a set of primes. A periodic group G is called a π-group if all prime divisors of the order of each of its elements lie in π. An action of G on a nontrivial group V is called free if, for any υ ∈ V and g ∈ G such that υg = υ, either υ = 1 or g = 1. We describe {2, 3}-groups that can act freely on an abelian group.
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Original Russian Text © A.Kh. Zhurtov, D.V. Lytkina, V.D.Mazurov, A.I. Sozutov, 2013, published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2013, Vol. 19, No. 3.
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Zhurtov, A.K., Lytkina, D.V., Mazurov, V.D. et al. Periodic groups acting freely on abelian groups. Proc. Steklov Inst. Math. 285 (Suppl 1), 209–215 (2014). https://doi.org/10.1134/S008154381405023X
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DOI: https://doi.org/10.1134/S008154381405023X