On accessible classes of groups and semigroups
Sbornik. Mathematics, Tome 19 (1973) no. 2, pp. 231-241 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this paper it is proved that any residually complete class of groups is either 1-step accessible in the class of all groups or is not $\gamma$-step accessible for any ordinal number $\gamma$, and there is given an extensive class of varieties of semigroups which cannot be $\gamma$-step accessible in the class of all semigroups. Bibliography: 15 titles.
@article{SM_1973_19_2_a7,
     author = {L. M. Martynov},
     title = {On accessible classes of groups and semigroups},
     journal = {Sbornik. Mathematics},
     pages = {231--241},
     year = {1973},
     volume = {19},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1973_19_2_a7/}
}
TY  - JOUR
AU  - L. M. Martynov
TI  - On accessible classes of groups and semigroups
JO  - Sbornik. Mathematics
PY  - 1973
SP  - 231
EP  - 241
VL  - 19
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_1973_19_2_a7/
LA  - en
ID  - SM_1973_19_2_a7
ER  - 
%0 Journal Article
%A L. M. Martynov
%T On accessible classes of groups and semigroups
%J Sbornik. Mathematics
%D 1973
%P 231-241
%V 19
%N 2
%U http://geodesic.mathdoc.fr/item/SM_1973_19_2_a7/
%G en
%F SM_1973_19_2_a7
L. M. Martynov. On accessible classes of groups and semigroups. Sbornik. Mathematics, Tome 19 (1973) no. 2, pp. 231-241. http://geodesic.mathdoc.fr/item/SM_1973_19_2_a7/

[1] L. N. Shevrin, L. M. Martynov, “O dostizhimykh klassakh algebr”, Sib. matem. zh., XII:6 (1971), 1363–1381

[2] A. I. Maltsev, “Ob umnozhenii klassov algebraicheskikh sistem”, Sib. matem. zh., VIII:2 (1967), 346–365

[3] A. I. Maltsev, Algebraicheskie sistemy, izd-vo «Nauka», Moskva, 1970 | MR

[4] A. I. Maltsev, “Obobschenno niltyutentnye algebry i ikh prisoedinennye gruppy”, Matem. sb., 25 (67) (1949), 347–366

[5] V. N. Salii, “Ekvatsionalno normalnye mnogoobraziya polugrupp”, Izv. VUZov, Matematika, 1969, no. 5, 61–68 | MR | Zbl

[6] B. I. Plotkin, “O funktorialakh, radikalakh i koradikalakh v gruppakh”, Matem. zap. Uralskogo un-ta, 7:3 (1970), 150–182 | MR | Zbl

[7] Kh. Neiman, Mnogoobraziya grupp, izd-vo «Mir», Moskva, 1969 | MR

[8] F. W. Levi, “Über die Untergruppen der freien Gruppen, II”, Math. Z., 37 (1933), 90–97 | DOI | MR | Zbl

[9] P. M. Neumann, “On the structure of standard wreath products of groups”, Math. Z., 84 (1964), 343–373 | DOI | MR | Zbl

[10] A. A. Vinogradov, “Kvazimnogoobraziya abelevykh grupp”, Algebra i logika, 4:6 (1965), 15–19 | MR | Zbl

[11] L. Ya. Kulikov, “Obobschennye primarnye gruppy, II”, Trudy Mosk. matem. ob-va, II (1953), 85–167 | MR

[12] L. Fuchs, “On the structure of abelian $p$-groups”, Acta Math. scient. Hungar, 4 (1953), 267–288 | DOI | MR | Zbl

[13] E. S. Lyapin, Polugruppy, Fizmatgiz, Moskva, 1960 | MR

[14] A. P. Biryukov, “Mnogoobraziya idempotentnykh polugrupp”, Algebra i logika, 9:3 (1970), 266–273

[15] J. A. Gerhard, “The lattice of equational classes of idempotent semigroups”, J. Algebra, 15:2 (1970), 195–224 | DOI | MR | Zbl