Geodesic
On groups which are the product of abelian subgroups
Glasgow mathematical journal, Tome 26 (1985) no. 2, pp. 151-156

Voir la notice de l'article provenant de la source Cambridge University Press

If the group G=AB is the product of two abelian subgroups A and B, then G is metabelian by a well-known result of Itô [8], so that the commutator subgroup G' of G is abelian. In the following we are concerned with the following condition:There exists a normal subgroupwhich is contained in A or B.Recently, Holt and Howlett in [7] have given an example of a countably infinite p-group G = AB, which is the product of two elementary abelian subgroups A and B with Core(A) = Core (B) = 1, so that in this group (*) does not hold. Also, Sysak in [13] gives an example of a product G = AB of two free abelian subgroups A and B with Core(A)=Core(B)=l. 
Amberg, Bernhard. On groups which are the product of abelian subgroups. Glasgow mathematical journal, Tome 26 (1985) no. 2, pp. 151-156. doi: 10.1017/S0017089500005929
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