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)
Mots clés : fully invariant subgroups, $\lambda $-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}, zbl = {1155.20053}, mrnumber = {2468040}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/ambp.244/} }
TY - JOUR AU - Danchev, Peter TI - On Some Fully Invariant Subgroups of Summable Groups JO - Annales mathématiques Blaise Pascal PY - 2008 SP - 147 EP - 152 VL - 15 IS - 2 PB - Annales mathématiques Blaise Pascal UR - http://archive.numdam.org/articles/10.5802/ambp.244/ DO - 10.5802/ambp.244 LA - en ID - AMBP_2008__15_2_147_0 ER -
%0 Journal Article %A Danchev, Peter %T On Some Fully Invariant Subgroups of Summable Groups %J Annales mathématiques Blaise Pascal %D 2008 %P 147-152 %V 15 %N 2 %I Annales mathématiques Blaise Pascal %U http://archive.numdam.org/articles/10.5802/ambp.244/ %R 10.5802/ambp.244 %G en %F 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://archive.numdam.org/articles/10.5802/ambp.244/
[1] Commutative group algebras of summable -groups, Commun. Algebra, Volume 35 (2007), pp. 1275-1289 | DOI | MR | Zbl
[2] Notes on -large subgroups of primary abelian groups and free valuated vector spaces, Bull. Allahabad Math. Soc., Volume 23 (2008), p. 149-154. | MR | Zbl
[3] On -large subgroups of summable -groups, Algebra Colloq., Volume 16 (2009)
[4] Infinite Abelian and Groups I, II, Mir, Moskva, 1974 and 1977 | MR | Zbl
[5] A note on -summable groups, Proc. Amer. Math. Soc., Volume 126 (1998), pp. 3133-3135 | DOI | MR | Zbl
[6] On fully invariant subgroups of primary abelian groups, Mich. Math. J., Volume 22 (1975), pp. 281-284 | MR | Zbl
[7] -large subgroups of -groups, Pac. J. Math., Volume 75 (1978), pp. 477-485 | MR | Zbl
[8] Extensions of totally projective groups, Proc. Amer. Math. Soc., Volume 64 (1977), pp. 35-38 | DOI | MR | Zbl
[9] The generalized Kulikov criterion, Can. J. Math., Volume 21 (1969), pp. 1192-1205 | DOI | MR | Zbl
[10] Homology and direct sums of countable abelian groups, Math. Z., Volume 101 (1967), pp. 182-212 | DOI | MR | Zbl
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