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The space which is composed by embedding countably many circles in such a way into the plane that their radii are given by a null-sequence and that they all have a common tangent point is called “The Hawaiian Earrings”. The fundamental group of this space is known to be a subgroup of the inverse limit of the finitely generated free groups, and it is known to be not free. Within the recent move of trying to get hands on the algebraic invariants of non-tame (e.g. non-triangulable) spaces this space...
We give an algebraic proof of the fact that a generating set of the mapping class group Mg,1 (g ≥ 3) may be obtained by replicating a generating set of M2,1.
We study the generation of finite groups by nilpotent subgroups and in particular we investigate the structure of groups which cannot be generated by nilpotent subgroups and such that every proper quotient can be generated by nilpotent subgroups. We obtain some results about the structure of these groups and a lower bound for their orders.
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