On Some Fully Invariant Subgroups of Summable Groups

Peter Danchev

doi:10.5802/ambp.244

Peter Danchev ¹

¹ Dept. of Mathematics and Statistics Plovdiv University 24 Tzar Assen Str. 4000 Plovdiv, BG BULGARIA

Annales mathématiques Blaise Pascal, Tome 15 (2008) no. 2, pp. 147-152.

Résumé

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)

MR Zbl

DOI : 10.5802/ambp.244

Classification : 20K10
Mots clés : fully invariant subgroups, $\lambda $-large subgroups, summable groups, free valuated vector spaces

Affiliations des auteurs :

Peter Danchev ¹

¹ Dept. of Mathematics and Statistics Plovdiv University 24 Tzar Assen Str. 4000 Plovdiv, BG BULGARIA

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Peter Danchev. 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. https://ambp.centre-mersenne.org/articles/10.5802/ambp.244/

Bibliographie
Cité par

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[2] P. Danchev 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 | Zbl

[3] P. Danchev On $λ$ -large subgroups of summable $C_{Ω}$ -groups, Algebra Colloq., Volume 16 (2009)

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[7] R. Linton $λ$ -large subgroups of $C_{λ}$ -groups, Pac. J. Math., Volume 75 (1978), pp. 477-485 | MR | Zbl

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

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

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