For a projectively invariant subgroup \(C\) of a reduced \(p\)-group \(G\), a nondecreasing sequence of ordinals and the symbol \(\infty\) is constructed in which the \(k\)th position, \(k=0,1,2,\dots\), is occupied by the minimum of heights in \(G\) of all nonzero elements of the subgroup \(p^kC[p]\). It is proved that if all elements of this sequence are integers, then the subgroup \(C\) is fully invariant.
This is a preview of subscription content, access via your institution.
Buy single article
Instant access to the full article PDF.
Tax calculation will be finalised during checkout.
C. Megibben, “Projection-invariant subgroups of Abelian groups,” Tamkang J. Math. 8 (2), 177–182 (1977).
J. Hausen, “Endomorphism rings generated by idempotents,” Tamkang J. Math. 12 (2), 215–218 (1981).
A. R. Chekhlov, “On projective invariant subgroups of Abelian groups,” J. Math. Sci. 164 (1), 143–147 (2010).
P. Danchev and B. Goldsmith, “On projective invariant subgroups of Abelian \(p\)-groups,” in Groups and Model Theory, Contemp. Math. (Amer. Math. Soc., Providence, RI, 2012), Vol. 576, pp. 31–40.
L. Fuchs, Infinite Abelian Groups (Academic Press, New York–London, 1970), Vol. 1.
A. L. S. Corner, “On endomorphism rings of primary abelian groups. II,” Quart. J. Math. Oxford Ser. (2) 27 (2), 5–13 (1976).
About this article
Cite this article
Chekhlov, A.R. Projectively Invariant Subgroups of Abelian \(p\)-Groups. Math Notes 109, 948–953 (2021). https://doi.org/10.1134/S000143462105028X
- projectively invariant subgroup
- fully invariant subgroup