On Some Fully Invariant Subgroups of Summable Groups

Danchev, Peter

doi:10.5802/ambp.244

Danchev, Peter 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 | 1 citation dans Numdam

DOI : 10.5802/ambp.244

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

Affiliations des auteurs :

Danchev, Peter ¹

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

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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/articles/10.5802/ambp.244/

Bibliographie
Cité par

[1] Danchev, P. Commutative group algebras of summable $p$ -groups, Commun. Algebra, Volume 35 (2007), pp. 1275-1289 | DOI | MR | Zbl

[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 | Zbl

[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 | Zbl

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

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

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

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

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

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

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