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# Prof. Dr. Felix Leinen - Publications

## Research Interests

 > Infinite groups with finiteness conditions. > Locally finite groups. > Ideal lattices in group rings of locally finite groups. > Infinite permutation groups. > Linear and finitary linear groups. > Finitary Lie algebras. > Residually finite and profinite groups. > Model theoretic notions in group theory. > Group theoretic constructions  (e.g. wreath products, permutational products).

## Publications

 [35] Positive definite functions of  finitary isometry groups over fields of odd characteristic,  J. Pure Appl. Algebra 208 (2007), 1003-1021  (with O. Puglisi). [34] Some results concerning simple locally finite groups of 1-type,  J. Algebra 287 (2005), 32-51  (with O. Puglisi). [33] Positive definite functions of diagonal limits of finite alternating groups, J. London Math. Soc. (2) 70 (2004), 678-690  (with O. Puglisi). [32] Diagonal limits of finite alternating groups: confined subgroups, ideals, and positive definite functions, Illinois J. Math. 47 (2003), 345-360  (with O. Puglisi). [31] Ideals in group algebras of simple locally finite groups of 1-type, Pacific J. Math. 207 (2002), 433-445  (with O. Puglisi). [30] Confined subgroups in periodic simple finitary linear groups, Israel J. Math. 128 (2002), 285-324  (with O. Puglisi). [29] Serial subalgebras of finitary Lie algebras, Proc. Amer. Math. Soc. 129 (2001), 45-51  (with O. Puglisi). [28] Irreducible finitary Lie algebras over fields of positive characteristic, Math. Proc. Camb. Phil. Soc. 129 (2000), 1-8  (with O. Puglisi). [27] Local systems in simple finitary Lie algebras, Comm. Algebra 28 (2000), 2887-2893. [26] Periodic groups covered by transitive subgroups of finitary permutations or by irreducible subgroups of finitary transformations, Trans. Amer. Math. Soc. 352 (2000), 1913-1934  (with O. Puglisi). [25] Finitary representations and images of transitive finitary permutation groups, J. Algebra 222 (1999), 524-549  (with O. Puglisi). [24] A reduction theorem for perfect locally finite minimal non-FC groups, Glasgow Math. J. 41 (1999), 81-83. [23] Irreducible finitary Lie algebras over fields of characteristic zero, J. Algebra 210 (1998), 697-702  (with O. Puglisi). [22] Countable recognizability of primitive periodic finitary linear groups, Math. Proc. Camb. Phil. Soc. 121 (1997), 425-435  (with O. Puglisi). [21] Irreducible representations of periodic finitary linear groups, J. Algebra 180 (1996), 517-529. [20] Existentially closed groups in specific classes, in: B. Hartley - G.M. Seitz - A.V. Borovik - R.M. Bryant (eds.), Finite and locally finite groups, NATO ASI Series C 471, Kluwer Acad. Publ., Dordrecht - Boston - London 1995, pp. 285-326  (survey article). [19] Absolute irreducibility for finitary linear groups, Rend. Sem. Mat. Univ. Padova 92 (1994), 59-61. [18] Hypercentral unipotent finitary skew linear groups, Comm. Algebra 22 (1994), 929-949. [17] Unipotent finitary linear groups, J. London Math. Soc. (2) 48 (1993), 59-76  (with O. Puglisi). [16] Countable closed LFC-groups with p-torsion, Trans. Amer. Math. Soc. 336 (1993), 193-217. [15] Existentially closed locally cofinite groups, Proc. Edinburgh Math. Soc. 35 (1992), 233-253. [14] Uncountable existentially closed groups in locally finite group classes, Glasgow Math. J. 32 (1990), 153-163. [13] Amalgamation of locally finite p-groups over a countable FC-group, Arch. Math. 52 (1989), 321-332. [12] Group rings of existentially closed locally finite p-groups, Publ. Math. Debrecen 35 (1988), 289-294. [11] Chief series and right regular representations of finite p-groups, J. Australian Math. Soc. (A) 44 (1988), 225-232. [10] An amalgamation theorem for soluble groups, Canadian Math. Bull. 30 (1987), 9-18. [9] Algebraically closed groups in locally finite group classes, in: O.H. Kegel - F. Menegazzo - G. Zacher (eds.), Group Theory, Proceedings Brixen/Bressanone 1986, Springer Lecture 1281, Berlin 1987, pp. 85-102  (with R.E. Phillips). [8] Algebraically closed locally finite groups, in: C.M. Campbell - E.F. Robertson (eds.), Groups - St. Andrews 1985, London Math. Soc. Lecture Notes 121, Cambridge 1986, pp. 246-248  (survey article). [7] A uniform way to control chief series in finite p-groups and to construct the countable algebraically closed locally finite p-groups, J. London Math. Soc. (2) 33 (1986), 260-270. [6] Existentially closed central extensions of locally finite p-groups, Math. Proc. Camb. Phil. Soc. 100 (1986), 281-301  (with R.E. Phillips). [5] Existentially closed locally finite p-groups, J. Algebra 103 (1986), 160-183. [4] Existentially closed LX-groups, Rend. Sem. Mat. Univ. Padova 75 (1986), 191-226. [3] Existentially closed groups in locally finite group classes, Comm. Algebra 13 (1985), 1991-2024. [2] Lokale Systeme in universellen Gruppen, Arch. Math. 41 (1983), 401-403. [1] Lokal endlich-pi-separierte Gruppen mit Minimalbedingung für Zentralisatoren, Arch. Math. 39 (1982), 407-413.