Abstract
We prove that anRN-group (in particular, locally solvable)G =G 1 G 2 ...G n withG i and π(G i ) ∩ π(G j ) = ⊘,i ≠j is a periodic hyper-Abelian group if the subgroupsG j are almost locally normal.
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References
N. S. Chernikov, “Groups factorizable in commuting periodic subgroups without elements of equal prime orders,” in:Investigations of Groups with Restrictions for Subgroups [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev, (1988), pp. 98–117.
N. S. Chernikov, “Solvability and local solvability of factorizableRN-groups,” in:Methods for Investigation of Algebraic and Topological Structures [in Russian], Kiev Pedagogical Institute, Kiev (1989), pp. 122–129.
N. S. Chernikov,Groups Factorizable into a Product of Commuting Subgroups [in Russian], Naukova Dumka, Kiev 1987.
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Chernikov, N.S. On groups factorizable in commuting almost locally normal subgroups. Ukr Math J 48, 480–482 (1996). https://doi.org/10.1007/BF02378539
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DOI: https://doi.org/10.1007/BF02378539