Mediterranean Journal of Mathematics

, Volume 8, Issue 3, pp 307–313 | Cite as

Periodic Endomorphisms of Polycyclic Groups

  • Gerard Endimioni


Let G be a polycyclic group. As a consequence of known results, any periodic group of automorphisms of G is finite and there is an upper bound (depending only on G) for its order. On the other hand, a periodic semigroup of endomorphisms of G need not be finite but we prove that it is locally finite. Also we show that the order of periodic endomorphisms of G is bounded.

Mathematics Subject Classification (2010)

20E15 20M20 


Polycyclic group periodic endomorphism periodic semigroup 


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Copyright information

© Springer Basel AG 2010

Authors and Affiliations

  1. 1.C.M.I.–Université de ProvenceMarseille Cedex 13France

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