We prove that the restricted wreath product Zn wr Z k has the R∞-property, i. e. every its automorphism Φ has infinite Reidemeister number R(Φ), in exactly two cases: (1) for any k and even n; (2) for odd k and n divisible by 3. In the remaining cases there are automorphisms with finite Reidemeister number, for which we prove the finite-dimensional twisted Burnside– Frobenius theorem (TBFTf ): R(Φ) is equal to the number of equivalence classes of finite-dimensional irreducible unitary representations fixed by the action [ρ] 7→ [ρ ? Φ].
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机译：我们证明了受限制的花圈产品Zn WR Z K具有r∞-属性，i。 e。每一套自动形态φ都有无限的Reideesister号码r（φ），在两个情况下：（1）对于任何k甚至n; （2）对于奇数k和n可被3划分。在剩下的情况下，存在有限的ReideEester号码的自同一性，我们证明了有限维扭曲的烧结吊架定理（TBFTF）：R（φ）等于数量Action [ρ] 7→[ρ]固定的有限维不可缩续的酉表示的等效类φ]。
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