Geodesic
Projectively Invariant Subgroups of Abelian $p$-Groups
Matematičeskie zametki, Tome 109 (2021) no. 6, pp. 921-928 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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.
Keywords: projection, projectively invariant subgroup, fully invariant subgroup. 
@article{MZM_2021_109_6_a10,
     author = {A. R. Chekhlov},
     title = {Projectively {Invariant} {Subgroups} of {Abelian} $p${-Groups}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {921--928},
     year = {2021},
     volume = {109},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2021_109_6_a10/}
}
TY  - JOUR
AU  - A. R. Chekhlov
TI  - Projectively Invariant Subgroups of Abelian $p$-Groups
JO  - Matematičeskie zametki
PY  - 2021
SP  - 921
EP  - 928
VL  - 109
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/MZM_2021_109_6_a10/
LA  - ru
ID  - MZM_2021_109_6_a10
ER  - 
%0 Journal Article
%A A. R. Chekhlov
%T Projectively Invariant Subgroups of Abelian $p$-Groups
%J Matematičeskie zametki
%D 2021
%P 921-928
%V 109
%N 6
%U http://geodesic.mathdoc.fr/item/MZM_2021_109_6_a10/
%G ru
%F MZM_2021_109_6_a10
A. R. Chekhlov. Projectively Invariant Subgroups of Abelian $p$-Groups. Matematičeskie zametki, Tome 109 (2021) no. 6, pp. 921-928. http://geodesic.mathdoc.fr/item/MZM_2021_109_6_a10/

[1] C. Megibben, “Projection-invariant subgroups of Abelian groups”, Tamkang J. Math., 8:2 (1977), 177–182 | MR

[2] J. Hausen, “Endomorphism rings generated by idempotents”, Tamkang J. Math., 12:2 (1981), 215–218 | MR

[3] A. R. Chekhlov, “O podgruppakh abelevykh grupp, invariantnykh otnositelno proektsii”, Fundament. i prikl. matem., 14:6 (2008), 211–218 | MR

[4] P. Danchev, B. Goldsmith, “On projective invariant subgroups of Abelian $p$-groups”, Groups and Model Theory, Contemp. Math., 576, Amer. Math. Soc., Providence, RI, 2012, 31–40 | DOI | MR

[5] L. Fuks, Beskonechnye abelevy gruppy, T. 1, Mir, M., 1974 | MR | Zbl

[6] A. L. S. Corner, “On endomorphism rings of primary abelian groups. II”, Quart. J. Math. Oxford Ser. (2), 27:2 (1976), 5–13 | DOI | MR