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Articles

Weakly fully and characteristically inert socle-regular Abelian p-groups

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Pages 4975-4987 | Received 01 Sep 2021, Accepted 07 May 2022, Published online: 28 May 2022

References

  • Carroll, D., Goldsmith, B. (1996). On transitive and fully transitive abelian p-groups. Proc. R. Irish Acad. (Math.). 96A(1):33–41. DOI: 10.2307/20490197.
  • Chekhlov, A. R. (2016). Fully inert subgroups of completely decomposable finite rank groups and their commensurability. Vestnik Tomskogo Gosudarstvennogo Universiteta. Matematika i Mekhanika. 41(3):42–50. (In Russian). DOI: 10.17223/19988621/41/4.
  • Chekhlov, A. R. (2017). On fully inert subgroups of completely decomposable groups. Math. Notes. 101(1–2):365–373. DOI: 10.1134/S0001434617010394.
  • Chekhlov, A. R. (2021). Projectively-invariant subgroups of Abelian p-groups. Math. Notes. 109(5–6):948–953. DOI: 10.1134/S000143462105028X.
  • Chekhlov, A. R., Danchev, P. V., Goldsmith, B. (2021). On the socles of fully inert subgroups of Abelian p-groups. Mediterr. J. Math. 18(3) DOI: 10.1007/s00009-021-01747-z.
  • Chekhlov, A. R., Danchev, P. V., Goldsmith, B. (2021). On the socles of characteristically inert subgroups of Abelian p-groups. Forum Math. 33(4):889–898. DOI: 10.1515/forum-2020-0348.
  • Corner, A. L. S. (1976). On endomorphism rings of primary Abelian groups II. Q. J. Math. 27(1):5–13. DOI: 10.1093/qmath/27.1.5.
  • Corner, A. L. S. (1976). The independence of Kaplansky’s notions of transitivity and full transitivity. Q. J. Math. 27(1):15–20. DOI: 10.1093/qmath/27.1.15.
  • Danchev, P., Goldsmith, B. (2009). On the socles of fully invariant subgroups of Abelian p-groups. Arch. Math. 92(3):191–199. DOI: 10.1007/s00013-009-3021-9.
  • Danchev, P., Goldsmith, B. (2010). On the socles of characteristic subgroups of Abelian p-groups. J. Algebra. 323(10):3020–3028. DOI: 10.1016/j.jalgebra.2009.12.005.
  • Dardano, U., Dikranjan, D., Salce, L. (2020). On uniformly fully inert subgroups of Abelian groups. Topol. Algebra Appl. 8(1):5–27. DOI: 10.1515/taa-2020-0002.
  • Dikranjan, D., Giordano Bruno, A., Salce, L., Virili, S. (2013). Fully inert subgroups of divisible Abelian groups. J. Group Theory. 16(6):915–939. DOI: 10.1515/jgt-2013-0014.
  • Dikranjan, D., Giordano Bruno, A., Salce, L., Virili, S. (2015). Intrinsic algebraic entropy. J. Pure Appl. Algebra 219(7):2933–2961. DOI: 10.1016/j.jpaa.2014.09.033.
  • Dikranjan, D., Salce, L., Zanardo, P. (2014). Fully inert subgroups of free Abelian groups. Period Math. Hung. 69(1):69–78. DOI: 10.1007/s10998-014-0041-4.
  • Dubois, P. F. (1971). Generally pα-torsion complete Abelain groups. Trans. Am. Math. Soc. 159:245–255. DOI: 10.1090/S0002-9947-1971-0280585-5.
  • Fuchs, L. (1958). Abelian Groups. Budapest: House of the Hungarian Academy of Sciences.
  • Fuchs, L. (1970, 1973). Infinite Abelian Groups, Vols. I and II. New York: Academic Press.
  • Fuchs, L. (2015). Abelian Groups. Cham: Springer, Switzerland.
  • Goldsmith, B., Salce, L. (2017). Algebraic entropies for Abelian groups with applications to their endomorphism rings: a survey. In: Droste, M., Fuchs, L., Goldsmith, B., Strüngmann, L., eds. Groups, Modules, and Model Theory–Surveys and Recent Developments. Cham: Springer, pp. 135–175. DOI: 10.1007/978-3-319-51718-6_7.
  • Goldsmith, B., Salce, L. (2020). Fully inert subgroups of torsion-complete p-groups. J. Algebra 555:406–424. DOI: 10.1016/j.jalgebra.2020.02.038.
  • Goldsmith, B., Salce, L. (2023). Abelian p-groups with minimal full inertia. Period. Math. Hung. 85 DOI: 10.1007/s10998-021-00414-w.
  • Goldsmith, B., Salce, L., Zanardo, P. (2014). Fully inert subgroups of Abelian p-groups. J. Algebra 419(1):332–349. DOI: 10.1016/j.jalgebra.2014.07.021.
  • Hausen, J., Johnson, J. A. (1981). Separability of sufficiently projective p-groups as reflected in their endomorphism rings. J. Algebra 69(2):270–280. DOI: 10.1016/0021-8693(81)90203-9.
  • Hill, P. D. (1969). On transitive and fully transitive primary groups. Proc. Am. Math. Soc. 22(2):414–417. DOI: 10.1090/S0002-9939-1969-0269735-0.
  • Kaplansky, I. (1954,1969). Infinite Abelian Groups. Ann Arbor: University of Michigan Press.
  • Keef, P. W. (2023). Countably totally projective Abelian p-groups have minimal full inertia. J. Comm. Algebra 15.
  • Pierce, R. S. (1963). Homomorphisms of Primary Abelian Groups. Chicago, IL: Topics in Abelian Groups, pp. 215–310.
  • Salce, L., Virili, S. (2018). Two new proofs concerning the intrinsic algebraic entropy. Commun. Algebra 46(9):3939–3949. DOI: 10.1080/00927872.2018.1430805.

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