Abstract
Niroomand (Arch. Math. 94 (2010) 401–404) proved a converse to a theorem of Schur in the following sense. He proved that if G is a group such that [G, G] is finite and G/Z(G) is finitely generated, then G/Z(G) is finite, of order bounded above by [G, G]k where k is the minimal number of generators required for G/Z(G). Here, we give a completely elementary short proof of a further generalization.
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Niroomand P.: The converse of Schur’s theorem. Arch. Math. 94, 401–404 (2010)
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In memory of Mrs. S. Devi
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Sury, B. A generalization of a converse to Schur’s theorem. Arch. Math. 95, 317–318 (2010). https://doi.org/10.1007/s00013-010-0180-7
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DOI: https://doi.org/10.1007/s00013-010-0180-7