Hyperzyklische gruppen |
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Authors: | Hermann Simon |
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Institution: | 1. Department of Mathematics, University of Miami, 33124, Coral Gables, Florida, (U.S.A.)
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Abstract: | Definition: (a)G is called hypercyclic «iff each epimorphic imageH≠1 ofG possesses a cyclic normal subgroupA≠1». (b)G is called hypercentral «iff each epimorphic imageH≠1 ofG hasZ(H)≠1». (c) the set of prime numbers which divide the orders of the torsion elements (≠1) ofG is called «the characteristic ofG». Baer has shown that each hypercyclic groupG is a subdirect product of hypercyclic groups of finite characteristic. In this note we will characterize hypercentral groups by abelian torsion groups of finite exponent. |
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