Twisted Conjugacy in Residually Finite Groups of Finite Prüfer Rank

The uploaded paper (Troitsky, arXiv:2210.00591v1, 2022) states and proves exactly the two targets: (A) the soluble-by-finite reduction for residually finite groups of finite upper rank with R(φ)<∞, and (B) TBFTf for residually finite groups of finite Prüfer rank. The candidate solution follows the same architecture: Jabara’s fixed-point bound in finite quotients plus Jaikin–Zapirain to get uniformly bounded-index soluble subgroups and a characteristic finite-index soluble pullback for (A) (matching the paper’s Section 2), and then the finite-quotient criterion, the finite-by-abelian/finite-inner-automorphism step, and induction on the derived length for (B) (matching the paper’s Lemma 1.9, Lemma 1.10, Cor. 1.11, Thm. 3.4, and Section 4). The only divergence is stylistic (e.g., the model invokes a Pontryagin-duality viewpoint for the abelian base, whereas the paper uses the “finite inner automorphisms” criterion); no missing hypotheses or substantive gaps are apparent. See Theorems A and B as stated and proved in the paper and the supporting lemmas cited therein .