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Keywords:
thick groups; pure subgroups; countable extensions; divisible groups; bounded groups
thick groups; pure subgroups; countable extensions; divisible groups; bounded groups
Summary:
We prove that pure subgroups of thick Abelian $p$-groups which are modulo countable are again thick. This generalizes a result due to Megibben (Michigan Math. J. 1966). Some related results are also established.
References:
[1] Benabdallah, K., Wilson, R.: Thick groups and essentially finitely indecomposable groups. Canad. J. Math. 30 (3) (1978), 650–654. DOI 10.4153/CJM-1978-056-9 | MR 0492006 | Zbl 0399.20049
[2] Danchev, P. V.: Commutative group algebras of thick abelian $p$-groups. Indian J. Pure Appl. Math. 36 (6) (2005), 319–328. MR 2178344 | Zbl 1088.20001
[3] Danchev, P. V.: Generalized Dieudonné and Hill criteria. Portugal. Math. 65 (1) (2008), 121–142. DOI 10.4171/PM/1802 | MR 2387091 | Zbl 1146.20034
[4] Danchev, P. V., Keef, P. W.: Generalized Wallace theorems. Math. Scand., to appear. MR 2498370
[5] Keef, P. W.: Primary abelian groups admitting only small homomorphisms. Commun. Algebra 23 (10) (1995), 3615–3626. DOI 10.1080/00927879508825421 | MR 1348253 | Zbl 0835.20072
[6] Megibben, C. K.: Large subgroups and small homomorphisms. Michigan Math. J. 13 (2) (1966), 153–160. DOI 10.1307/mmj/1028999539 | MR 0195939 | Zbl 0166.02502
[7] Nunke, R. J.: Homology and direct sums of countable abelian groups. Math. Z. 101 (3) (1967), 182–212. DOI 10.1007/BF01135839 | MR 0218452 | Zbl 0173.02401
[8] Pierce, R. S.: Homomorphisms of Primary Abelian Groups, Topics in Abelian Groups. (Proc. Sympos., New Mexico State Univ., 1962), Scott, Foresman and Co., Chicago, Illinois, 1963, pp. 215–310. MR 0177035
[9] Wallace, K. D.: On mixed groups of torsion-free rank one with totally projective primary components. J. Algebra 17 (4) (1971), 482–488. DOI 10.1016/0021-8693(71)90005-6 | MR 0272891 | Zbl 0215.39902
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