Geodesic
Subgroups, automorphisms, and Lie algebras related to the basis-conjugating automorphism group
Algebra i logika, Tome 55 (2016) no. 6, pp. 670-703.

Voir la notice de l'article provenant de la source Math-Net.Ru

We study some subgroups of the automorphism group of a free group, their factorizations into a semidirect product, automorphism groups, and adjoint Lie algebras.
Keywords: free group, Lie algebra.
Mots-clés : automorphism group 
@article{AL_2016_55_6_a1,
     author = {V. G. Bardakov and M. V. Neshchadim},
     title = {Subgroups, automorphisms, and {Lie} algebras related to the basis-conjugating automorphism group},
     journal = {Algebra i logika},
     pages = {670--703},
     publisher = {mathdoc},
     volume = {55},
     number = {6},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2016_55_6_a1/}
}
TY  - JOUR
AU  - V. G. Bardakov
AU  - M. V. Neshchadim
TI  - Subgroups, automorphisms, and Lie algebras related to the basis-conjugating automorphism group
JO  - Algebra i logika
PY  - 2016
SP  - 670
EP  - 703
VL  - 55
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AL_2016_55_6_a1/
LA  - ru
ID  - AL_2016_55_6_a1
ER  - 
%0 Journal Article
%A V. G. Bardakov
%A M. V. Neshchadim
%T Subgroups, automorphisms, and Lie algebras related to the basis-conjugating automorphism group
%J Algebra i logika
%D 2016
%P 670-703
%V 55
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AL_2016_55_6_a1/
%G ru
%F AL_2016_55_6_a1
V. G. Bardakov; M. V. Neshchadim. Subgroups, automorphisms, and Lie algebras related to the basis-conjugating automorphism group. Algebra i logika, Tome 55 (2016) no. 6, pp. 670-703. http://geodesic.mathdoc.fr/item/AL_2016_55_6_a1/

[1] S. Krstic, J. McCool, “The non-finite presentability of $\mathrm{IA}(F_3)$ and $\mathrm{GL}_2(\mathbb Z[t,t^{-1}])$”, Invent. Math., 129:3 (1997), 595–606 | DOI | MR | Zbl

[2] O. Chein, “Subgroups of IA automorphisms of a free group”, Acta Math., 123 (1969), 1–12 | DOI | MR

[3] J. McCool, “On basis-conjugating automorphisms of free groups”, Can. J. Math., 38:6 (1986), 1525–1529 | DOI | MR | Zbl

[4] A. G. Savushkina, “Sopryagayuschie bazis avtomorfizmy svobodnoi gruppy”, Vestn. Mosk. un-ta. Ser. 1. Matem. Mekhan., 1996, no. 4, 17–21 | MR | Zbl

[5] V. G. Bardakov, “Stroenie gruppy sopryagayuschikh avtomorfizmov”, Algebra i logika, 42:5 (2003), 515–541 | MR | Zbl

[6] A. Lubotsky, “Normal automorphisms of free groups”, J. Algebra, 63:2 (1980), 494–498 | DOI | MR

[7] A. S.-T. Lue, “Normal automorphisms of free groups”, J. Algebra, 64:1 (1980), 52–53 | DOI | MR | Zbl

[8] M. V. Neschadim, “Svobodnye proizvedeniya grupp ne imeyut vneshnikh normalnykh avtomorfizmov”, Algebra i logika, 35:5 (1996), 562–566 | MR

[9] M. V. Neschadim, Normalnye avtomorfizmy grupp kos, Preprint No 4, In-t matem. SO RAN, Novosibirsk, 1993

[10] M. V. Neschadim, “Ob otsutstvii vneshnikh normalnykh avtomorfizmov u nekotorykh grupp avtomorfizmov”, Mezhvuzovskii sb., Novosibirskii gos. un-t, 1995, 48–61

[11] E. I. Khukhro, Nilpotent groups and their automorphisms, de Gruyter Exp. Math., 8, Walter de Gruyter, Berlin, 1993 | MR | Zbl

[12] F. R. Cohen, J. Pakianathan, V. V. Vershinin, J. Wu, “Basis-conjugating automorphisms of a free group and associated Lie algebras”, Proc. conf. groups, homotopy and configuration spaces (Univ. of Tokyo, July, 2005 in honor of the 60th birthday of F. Cohen), Geom. Topol. Monogr., 13, eds. N. Iwase et al., Geom. Topol. Publ., Coventry, 2008, 147–168 | DOI | MR | Zbl

[13] V. G. Bardakov, R. Mikhailov, V. V. Vershinin, J. Wu, “On the pure virtual braid group $PV_3$”, Commun. Algebra, 44:3 (2016), 1350–1378 | DOI | MR | Zbl

[14] R. Lindon, P. Shupp, Kombinatornaya teoriya grupp, Mir, M., 1980

[15] V. G. Bardakov pThe virtual and universal braids, Fundam. Math., 181 (2004), 1–18 | DOI | MR

[16] A. G. Savushkina, “O gruppe sopryagayuschikh avtomorfizmov svobodnoi gruppy”, Matem. zametki, 60:1 (1996), 92–108 | DOI | MR | Zbl

[17] A. A. Markov, Osnovy algebraicheskoi teorii kos, Tr. matem. in-ta im. V. A. Steklova, 16, Izd-vo AN SSSR, M.–L., 1945 | MR | Zbl

[18] W. Magnus, A. Karrass, D. Solitar, Combinatorial group theory. Presentations of groups in terms of generators and relations, Dover Books Adv. Math., 2nd rev. ed., Dover Publ., New York, 1976 | MR | Zbl

[19] T. Kohno, “Série de Poincaré–Koszul associée aux groupes de tresses pures”, Invent. Math., 82:1 (1985), 57–75 | DOI | MR | Zbl

[20] M. Falk, R. Randell, “The lower central series of a fiber type arrangement”, Invent. Math., 82 (1985), 77–88 | DOI | MR | Zbl

[21] T. Kohno, “Linear representations of braid groups and classical Yang–Baxter equations”, Braids, AMS–IMS–SIAM Jt. Summer Res. Conf. (Santa Cruz/Calif. 1986), Contemp. Math., 78, Am. Math. Soc., Providence, RI, 1988, 339–363 | DOI | MR | Zbl

[22] T. Kohno, “Vassiliev invariants and de Rham complex on the space of knots”, Symplectic geometry and quantization, Papers presented at the 31st Taniguchi int. symp. symplectic geometry and quantization problems (Sanda, Japan, July 12–17, 1993) and a satellite symp. (Keio Univ., Yokohama, Japan, July 21–24, 1993), Contemp. Math., 179, eds. Y. Maeda et al., Am. Math. Soc., Providence, RI, 1994 | MR | Zbl

[23] C. Jensen, J. McCammond, J. Meier, “The integral cohomology of the group of loops”, Geom. Topol., 10 (2006), 759–784 | DOI | MR | Zbl

[24] C. D. H. Cooper, “Power automorphisms of a group”, Math. Z., 107:5 (1968), 335–356 | DOI | MR | Zbl