We study some subgroups of the automorphism group of a free group, their factorizations into a semidirect product, automorphism groups, and adjoint Lie algebras.
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S. Krstic and J. McCool, “The non-finite presentability of IA(F3) and \( {\mathrm{GL}}_2\left(\mathrm{\mathbb{Z}}\left[t,{t}^{-1}\right]\right) \),” Inv. Math., 129, No. 3, 595-606 (1997).
O. Chein, “Subgroups of IA automorphisms of a free group,” Acta Math., 123, 1-12 (1969).
J. McCool, “On basis-conjugating automorphisms of free groups,” Can. J. Math., 38, No. 6, 1525-1529 (1986).
A. G. Savushkina, “Basis-conjugating automorphisms of a free group,” Vest. MGU, Ser. 1, Mat. Mekh., No. 4, 17-21 (1996).
V. G. Bardakov, “Structure of a conjugating automorphism group,” Algebra and Logic, 42, No. 5, 287-303 (2003).
A. Lubotzky, “Normal automorphisms of free groups,” J. Alg., 63, No. 2, 494-498 (1980).
A. S.-T. Lue, “Normal automorphisms of free groups,” J. Algebra, 64, No. 1, 52-53 (1980).
M. V. Neshchadim, “Free products of groups have no outer normal automorphisms,” Algebra and Logic, 35, No. 5, 316-318 (1996).
M. V. Neshchadim, Normal Automorphisms of Braid Groups [in Russian], Preprint No. 4, Sobolev Institute of Mathematics, Novosibirsk (1993).
M. V. Neshchadim, “Some automorphism groups have no outer normal automorphisms,” in Mezhvuz. Sbornik [in Russian], NGU, Novosibirsk (1995), pp. 48-61.
E. I. Khukhro, Nilpotent Groups and Their Automorphisms, de Gruyter Exp. Math., 8, Walter de Gruyter, Berlin (1993).
F. R. Cohen, J. Pakianathan, V. V. Vershinin, and J. Wu, “Basis-conjugating automorphisms of a free group and associated Lie algebras,” in Geom. Topol. Monogr., 13, Geom. Topol. Publ., Coventry (2008), pp. 147-168.
V. G. Bardakov, R. Mikhailov, V. V. Vershinin, and J. Wu, “On the pure virtual braid group PV 3,” Comm. Alg., 44, No. 3, 1350-1378 (2016).
R. C. Lyndon and P. E. Schupp, Combinatorial Group Theory, Springer, Berlin (1977).
V. G. Bardakov, “The virtual and universal braids,” Fund. Math., 181, 1-18 (2004).
A. G. Savushkina, “The conjugating automorphism group of a free group,” Mat. Zametki, 60, No. 1, 92-108 (1996).
A. A. Markov, “Fundamentals of algebraic theory of braid groups,” Trudy Mat. Inst. Akad. Nauk SSSR, 16, 1-54 (1945).
W. Magnus, A. Karrass, and D. Solitar, Combinatorial Group Theory. Presentations of Groups in Terms of Generators and Relations, 2nd rev. ed., Dover Books Adv. Math., Dover Publ., New York (1976).
T. Kohno, “Série de Poincaré–Koszul associée aux groupes de tresses pures,” Inv. Math., 82, No. 1, 57-75 (1985).
M. Falk and R. Randell, “The lower central series of a fiber type arrangement,” Inv. Math., 82, 77-88 (1985).
T. Kohno, “Linear representations of braid groups and classical Yang–Baxter equations,” in Cont. Math., 78, Am. Math. Soc., Providence, RI (1988), pp. 339-363.
T. Kohno, “Vassiliev invariants and de Rham complex on the space of knots,” in Cont. Math., 179, Am. Math. Soc., Providence, RI (1994), pp. 123-138.
C. Jensen, J. McCammond, and J. Meier, “The integral cohomology of the group of loops,” Geom. Topol., 10, 759-784 (2006).
C. D. H. Cooper, “Power automorphisms of a group,” Math. Z., 107, No. 5, 335-356 (1968).
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(V. G. Bardakov, M. V. Neshchadim) Supported by RFBR (projects No. 13-01-00513, 14-01-00014, and 15-01-0745) and by Laboratory of Quantum Topology, Chelyabinsk State University (RF Government grant No. 14.Z50.31.0020).
Translated from Algebra i Logika, Vol. 55, No. 6, pp. 670-703, November-December, 2016.
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Bardakov, V.G., Neshchadim, M.V. Subgroups, Automorphisms, and Lie Algebras Related to the Basis-Conjugating Automorphism Group. Algebra Logic 55, 436–460 (2017). https://doi.org/10.1007/s10469-017-9417-x
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DOI: https://doi.org/10.1007/s10469-017-9417-x