Groups defined by periodic paired relations
Sbornik. Mathematics, Tome 188 (1997) no. 9, pp. 1269-1278 Cet article a éte moissonné depuis la source Math-Net.Ru

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The class of groups defined by periodic paired relations includes the Coxeter groups and the generalized triangle groups. In this paper generalizations are proved for this class of groups of several theorems that are known for Coxeter groups and generalized triangle groups.
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È. B. Vinberg. Groups defined by periodic paired relations. Sbornik. Mathematics, Tome 188 (1997) no. 9, pp. 1269-1278. http://geodesic.mathdoc.fr/item/SM_1997_188_9_a0/

[1] Selberg A., “O diskretnykh gruppakh preobrazovanii simmetricheskikh prostranstv bolshoi razmernosti”, Matematika, 6:3 (1962), 3–15

[2] Thomas R. M., “Cayley graphs and group presentations”, Math. Proc. Cambridge Phil. Soc., 103:3 (1988), 385–387 | DOI | MR | Zbl

[3] Baumslag G., Morgan J. W., Shalen P. B., “Generalized triangle groups”, Math. Proc. Cambridge Phil. Soc., 102:1 (1987), 25–31 | DOI | MR | Zbl

[4] Coxeter H. S. M., “The complete enumeration of finite groups of the form $R_i^2=(R_iR_j)^{k_{ij}}=\nobreak 1$”, J. London Math. Soc., 10 (1935), 21–25 | DOI | Zbl

[5] Burbaki N., Gruppy i algebry Li, Gl. IV–VI, Mir, M., 1972 | MR | Zbl

[6] Fine B., Rosenberger G., “A note on generalized triangle groups”, Abh. Math. Sem. Univ. Hamburg, 56 (1986), 233–244 | DOI | MR | Zbl

[7] Fine B., Howie J., Rosenberger G., “One-relator quotients and free products of cyclics”, Proc. Amer. Math. Soc., 102:2 (1988), 249–254 | DOI | MR | Zbl

[8] Howie J., Metaftsis V., Thomas R. M., “Finite generalized triangle groups”, Trans. Amer. Math. Soc., 347:9 (1995), 3613–3623 | DOI | MR | Zbl

[9] Lévai L., Rosenberger G., Souvignier B., “All finite generalized triangle groups”, Trans. Amer. Math. Soc. (to appear) | MR

[10] Tsaranov S. V., “On a generalization of Coxeter groups”, Algebras, Groups and Geometries, 6 (1989), 281–318 | MR | Zbl

[11] Tsaranov S. V., “Finite generalized Coxeter groups”, Algebras, Groups and Geometries, 6 (1989), 421–452 | MR | Zbl

[12] Baumslag B., Pride S. J., “Groups with two more generators than relators”, J. London Math. Soc., 17 (1978), 425–426 | DOI | MR | Zbl

[13] Veil G., Klassicheskie gruppy, ikh invarianty i predstavleniya, IL, M., 1947

[14] Razmyslov Yu. P., “Tozhdestva so sledom polnykh matrichnykh algebr nad polem kharakteristiki $0$”, Izv. AN. SSSR. Ser. matem., 38:4 (1974), 723–756 | MR | Zbl

[15] Procesi C., “The invariant theory of $n\times n$ matrices”, Adv. in Math., 19 (1976), 306–381 | DOI | MR | Zbl

[16] Vinberg E. B., Popov V. L., “Teoriya invariantov”, Itogi nauki i tekhniki. Sovr. probl. matem. Fundam. napravl., 55, VINITI, M., 1989, 137–309 | MR