Geodesic
Identities of almost stable group representations
Sbornik. Mathematics, Tome 60 (1988) no. 2, pp. 569-581 
Vovsi S. M.; Nguyen Hung Son. Identities of almost stable group representations. Sbornik. Mathematics, Tome 60 (1988) no. 2, pp. 569-581. http://geodesic.mathdoc.fr/item/SM_1988_60_2_a19/
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Voir la notice de l'article provenant de la source Math-Net.Ru

It is proved that almost stable group representations over a field have a finite basis of identities. Moreover, a variety generated by an arbitrary almost stable representation is Specht and all of its subvarieties have a finite uniformly bounded basis rank. In particular, the identities of an arbitrary representation of a finite group are finitely based. Bibliography: 17 titles.

[1] Olshanskii A. Yu., “O probleme konechnogo bazisa tozhdestv v gruppakh”, Izv. AN SSSR. Ser. mat., 34:2 (1970), 376–384

[2] Grinberg A. S., “Dva zamechaniya o mnogoobraziyakh par”, Latv. matem. ezhegodnik, 13 (1973), 64–74 | MR | Zbl

[3] Vovsi S. M., “O kriticheskikh predstavleniyakh grupp”, Latv. matem. ezhegodnik, 20, 1976, 141–159 | MR

[4] Plotkin B. I., “Lokalno konechnye i lokalno ogranichennye mnogoobraziya par – predstavlenii grupp”, Sb. rabot po algebre, Riga, 1978, 188–245 | MR | Zbl

[5] Volkov M. V., Gein A. G., “Tozhdestva pochti nilpotentnykh kolets Li”, Matem. sb., 118(160) (1982), 132–142 | MR | Zbl

[6] Kruse R. L., “Identities satisfied by a finite ring”, J. Algebre, 26:2 (1973), 298–318 | DOI | MR | Zbl

[7] Cosseu J., “Laws in nilpotent-by-finite groups”, Proc. Amer. Math. Soc., 19:3 (1968), 685–688 | DOI | MR

[8] Plotkin B. I., Vovsi S. M., Mnogoobraziya predstavlenii grupp: obschaya teoriya, svyazi i prilozheniya, Zinatne, Riga, 1983 | MR | Zbl

[9] Gringlaz L. Ya., “O lokalno ogranichennykh mnogoobraziyakh par”, Nekotorye voprosy teorii grupp, LGU, Riga, 1971, 19–27 | MR

[10] Oates S., Powel M. B., “Identical relations in finite groups”, J. Algebra, 1:1 (1964), 11–39 | DOI | MR | Zbl

[11] Neiman Kh., Mnogoobraziya grupp, Mir, M., 1969 | MR

[12] Platonov V. P., “Podgruppa Frattini lineinykh grupp i finitnaya approksimiruemost”, DAN SSSR, 171:4 (1966), 798–801 | MR | Zbl

[13] Gaschütz W., “Über die $\Phi$-untergruppe endliecher Groppen”, Math. Z., 58 (1953), 160–170 | DOI | MR | Zbl

[14] Kovacs L. G., Newman M. F., “Cross varieties of groups”, Proc. Roy. Soc. (London). A, 292 (1966), 530–536 | DOI | MR | Zbl

[15] Suprunenko D. A., Gruppy matrits, Nauka, M., 1972 | MR

[16] Baumslag G., “Wreath products and $p$-groups”, Proc. Cambridge Publ. Soc., 55:3 (1959), 224–231 | DOI | MR | Zbl

[17] Maltsev A. I., “O nekotorykh klassakh beskonechnykh razreshimykh grupp”, Matem. sb., 28(70) (1951), 567–588