On Some Fully Invariant Subgroups of Summable Groups
Danchev, Peter
Annales mathématiques Blaise Pascal, Tome 15 (2008), p. 147-152 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)

We show the inheritance of summable property for certain fully invariant subgroups by the whole group and vice versa. The results are somewhat parallel to these due to Linton (Mich. Math. J., 1975) and Linton-Megibben (Proc. Amer. Math. Soc., 1977). They also generalize recent assertions of ours in (Alg. Colloq., 2009) and (Bull. Allah. Math. Soc., 2008)

Publié le : 2008-01-01
DOI : https://doi.org/10.5802/ambp.244
Classification:  20K10 
@article{AMBP_2008__15_2_147_0,
     author = {Danchev, Peter},
     title = {On Some Fully Invariant Subgroups of Summable Groups},
     journal = {Annales math\'ematiques Blaise Pascal},
     volume = {15},
     year = {2008},
     pages = {147-152},
     doi = {10.5802/ambp.244},
     zbl = {1155.20053},
     mrnumber = {2468040},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AMBP_2008__15_2_147_0}
}

Danchev, Peter. On Some Fully Invariant Subgroups of Summable Groups. Annales mathématiques Blaise Pascal, Tome 15 (2008) pp. 147-152. doi : 10.5802/ambp.244. http://gdmltest.u-ga.fr/item/AMBP_2008__15_2_147_0/

[1] Danchev, P. Commutative group algebras of summable p-groups, Commun. Algebra, Tome 35 (2007), pp. 1275-1289 | Article | MR 2313667 | Zbl 1122.20003

[2] Danchev, P. Notes on λ-large subgroups of primary abelian groups and free valuated vector spaces, Bull. Allahabad Math. Soc., Tome 23 (2008), p. 149-154. | MR 2405840 | Zbl 1163.20034

[3] Danchev, P. On λ-large subgroups of summable C Ω -groups, Algebra Colloq., Tome 16 (2009)

[4] Fuchs, L. Infinite Abelian and Groups I, II, Mir, Moskva (1974 and 1977) | MR 457533 | Zbl 0274.20067

[5] Hill, P. A note on σ-summable groups, Proc. Amer. Math. Soc., Tome 126 (1998), pp. 3133-3135 | Article | MR 1476137 | Zbl 0907.20048

[6] Linton, R. On fully invariant subgroups of primary abelian groups, Mich. Math. J., Tome 22 (1975), pp. 281-284 | MR 396788 | Zbl 0308.20041

[7] Linton, R. λ-large subgroups of C λ -groups, Pac. J. Math., Tome 75 (1978), pp. 477-485 | MR 507070 | Zbl 0392.20035

[8] Linton, R.; Megibben, C. Extensions of totally projective groups, Proc. Amer. Math. Soc., Tome 64 (1977), pp. 35-38 | Article | MR 450425 | Zbl 0386.20028

[9] Megibben, C. The generalized Kulikov criterion, Can. J. Math., Tome 21 (1969), pp. 1192-1205 | Article | MR 249509 | Zbl 0208.03502

[10] Nunke, R. Homology and direct sums of countable abelian groups, Math. Z., Tome 101 (1967), pp. 182-212 | Article | MR 218452 | Zbl 0173.02401