Adjoining cofinitary permutations (II)

 We construct several forcing models in each of which there exists a maximal cofinitary group, i.e., a maximal almost disjoint group, G≤Sym(ℕ), such that G is also a maximal almost disjoint family in Sym(ℕ). We also ask several open questions in this area in the fourth section of this paper. Received: 25 December 2000 / Revised version: 10 December 2001 Published online: 5 November 2002 Current address:Department of Mathematics, University of Michigan, Ann Arbor, MI, 48109-1109. USA.e-mail: yizhang@umich.edu The author's research on this subject was partially supported by a visiting grant from the Institute Mittag–Leffler, Royal Academy of Science, Sweden and the grant no. 40734 of Academy of Finland. Mathematics Subject Classification (2000): 03E35, 20A15, 20B07, 20B35