On Some Fully Invariant Subgroups of Summable Groups
Annales Mathématiques Blaise Pascal, Tome 15 (2008) no. 2, pp. 147-152.

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)

DOI : https://doi.org/10.5802/ambp.244
Classification : 20K10
Mots clés : fully invariant subgroups, λ-large subgroups, summable groups, free valuated vector spaces
@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},
     pages = {147--152},
     publisher = {Annales math\'ematiques Blaise Pascal},
     volume = {15},
     number = {2},
     year = {2008},
     doi = {10.5802/ambp.244},
     mrnumber = {2468040},
     zbl = {1155.20053},
     language = {en},
     url = {www.numdam.org/item/AMBP_2008__15_2_147_0/}
}
Danchev, Peter. On Some Fully Invariant Subgroups of Summable Groups. Annales Mathématiques Blaise Pascal, Tome 15 (2008) no. 2, pp. 147-152. doi : 10.5802/ambp.244. http://www.numdam.org/item/AMBP_2008__15_2_147_0/

[1] Danchev, P. Commutative group algebras of summable p-groups, Commun. Algebra, Volume 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., Volume 23 (2008), p. 149-154. | MR 2405840 | Zbl 1163.20034

[3] Danchev, P. On λ-large subgroups of summable C Ω -groups, Algebra Colloq., Volume 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., Volume 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., Volume 22 (1975), pp. 281-284 | MR 396788 | Zbl 0308.20041

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

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

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

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