Relative holomorphs of free abelian groups and their invariant subgroups
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 4 (2015), pp. 41-45
Cet article a éte moissonné depuis la source Math-Net.Ru
This article focuses on invariant subgroups of the relative holomorph of an abelian group. Some properties of an invariant subgroup of the relative holomorph are proved. We also prove that a free abelian group is determined by its relative holomorph.
Keywords:
holomorph, relative holomorph, free abelian group, invariant subgroup, relative holomorphically isomorphic groups.
@article{VTGU_2015_4_a4,
author = {A. V. Razina},
title = {Relative holomorphs of free abelian groups and their invariant subgroups},
journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
pages = {41--45},
year = {2015},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VTGU_2015_4_a4/}
}
A. V. Razina. Relative holomorphs of free abelian groups and their invariant subgroups. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 4 (2015), pp. 41-45. http://geodesic.mathdoc.fr/item/VTGU_2015_4_a4/
[1] Bekker I. Kh., “O golomorfakh abelevykh grupp”, Sib. matem. zhurn., 5:6 (1964), 1228–1238 (in Russian) | MR | Zbl
[2] Grinshpon I. E., “Normal'nye podgruppy golomorfov abelevykh grupp i pochti golomorfnyy izomorfizm”, Fundament. i prikl. matem., 13:3 (2007), 9–16 (in Russian) | MR
[3] Grinshpon S. Ya., “Pochti golomorfno izomorfnye abelevy gruppy”, Voprosy matematiki, Trudy TGU, 220, no. 3, 1975, 78–84 (in Russian) | MR
[4] Mills W. H., “Multiple holomorph of finitely generated abelian groups”, Trans. Amer. Math. Soc., 71:3 (1950), 379–392 | DOI | MR
[5] Fuks L., Beskonechnye abelevy gruppy, v. 2, Mir Publ., M., 1974, 416 pp. (in Russian)