On Some Fully Invariant Subgroups of Summable Groups

Peter Danchev[1]

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

Annales mathématiques Blaise Pascal (2008)

  • Volume: 15, Issue: 2, page 147-152
  • ISSN: 1259-1734

Abstract

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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)

How to cite

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Danchev, Peter. "On Some Fully Invariant Subgroups of Summable Groups." Annales mathématiques Blaise Pascal 15.2 (2008): 147-152. <http://eudml.org/doc/10557>.

@article{Danchev2008,
abstract = {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)},
affiliation = {Dept. of Mathematics and Statistics Plovdiv University 24 Tzar Assen Str. 4000 Plovdiv, BG BULGARIA},
author = {Danchev, Peter},
journal = {Annales mathématiques Blaise Pascal},
keywords = {fully invariant subgroups; $\lambda $-large subgroups; summable groups; free valuated vector spaces; large subgroups},
language = {eng},
month = {7},
number = {2},
pages = {147-152},
publisher = {Annales mathématiques Blaise Pascal},
title = {On Some Fully Invariant Subgroups of Summable Groups},
url = {http://eudml.org/doc/10557},
volume = {15},
year = {2008},
}

TY - JOUR
AU - Danchev, Peter
TI - On Some Fully Invariant Subgroups of Summable Groups
JO - Annales mathématiques Blaise Pascal
DA - 2008/7//
PB - Annales mathématiques Blaise Pascal
VL - 15
IS - 2
SP - 147
EP - 152
AB - 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)
LA - eng
KW - fully invariant subgroups; $\lambda $-large subgroups; summable groups; free valuated vector spaces; large subgroups
UR - http://eudml.org/doc/10557
ER -

References

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  1. P. Danchev, Commutative group algebras of summable p -groups, Commun. Algebra 35 (2007), 1275-1289 Zbl1122.20003MR2313667
  2. P. Danchev, Notes on λ -large subgroups of primary abelian groups and free valuated vector spaces, Bull. Allahabad Math. Soc. 23 (2008), 149-154. Zbl1163.20034MR2405840
  3. P. Danchev, On λ -large subgroups of summable C Ω -groups, Algebra Colloq. 16 (2009) Zbl1176.20055
  4. L. Fuchs, Infinite Abelian and Groups I, II, (1974 and 1977), Mir, Moskva Zbl0274.20067MR457533
  5. P. Hill, A note on σ -summable groups, Proc. Amer. Math. Soc. 126 (1998), 3133-3135 Zbl0907.20048MR1476137
  6. R. Linton, On fully invariant subgroups of primary abelian groups, Mich. Math. J. 22 (1975), 281-284 Zbl0308.20041MR396788
  7. R. Linton, λ -large subgroups of C λ -groups, Pac. J. Math. 75 (1978), 477-485 Zbl0392.20035MR507070
  8. R. Linton, C. Megibben, Extensions of totally projective groups, Proc. Amer. Math. Soc. 64 (1977), 35-38 Zbl0386.20028MR450425
  9. C. Megibben, The generalized Kulikov criterion, Can. J. Math. 21 (1969), 1192-1205 Zbl0208.03502MR249509
  10. R. Nunke, Homology and direct sums of countable abelian groups, Math. Z. 101 (1967), 182-212 Zbl0173.02401MR218452

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