Bounds for the index of the centre in capable groups |
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| Authors: | K Podoski B Szegedy |
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| Institution: | Department of Algebra and Number Theory, Eötvös University, Pázmány Péter sétány 1/c, H-1117 Budapest, Hungary ; Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, POB 127, H-1364 Budapest, Hungary |
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| Abstract: | A group  is called capable if it is isomorphic to  for some group  . Let  be a capable group. I. M. Isaacs (2001) showed that if  is finite, then the index of the centre is bounded above by some function of  . We show that if  , then  with some constant  and this bound is essentially best possible. We complete a result of Isaacs, showing that if  is a cyclic group, then  . |
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