Geodesic
Projectively Invariant Subgroups of Abelian $p$-Groups
Matematičeskie zametki, Tome 109 (2021) no. 6, pp. 921-928

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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},
     publisher = {mathdoc},
     volume = {109},
     number = {6},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2021_109_6_a10/}
}
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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/