Quasibases for nonseparable p-groups
Rendiconti del Seminario Matematico della Università di Padova, Tome 144 (2020), pp. 197-215.
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This paper is an extension of the work developed in [4] on quasibases of abelian p-groups and based on the doctoral dissertation ofAndrija Vodopivec [5].We introduce the ideas of a δ-combination and height of an inductive quasibasis and show that the height of a quasibasis is invariant for related inductive quasibases. Moreover, an abelian p-group is separable if and only if the heights of all δ-combinations are zero. Finally, we show that an abelian p-group is not reduced if and only if there exists a δ-combination with infinite height.

Publié le :
DOI : 10.4171/rsmup/65
Classification : 20, 00 
@article{RSMUP_2020__144__197_0,
     author = {Otto Mutzbauer and Elias Toubassi and Andrija Vodopivec},
     title = {Quasibases for nonseparable $p$-groups},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {197--215},
     volume = {144},
     year = {2020},
     doi = {10.4171/rsmup/65},
     mrnumber = {4186455},
     zbl = {1507.20027},
     language = {en},
     url = {http://www.numdam.org/articles/10.4171/rsmup/65/}
}
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%J Rendiconti del Seminario Matematico della Università di Padova
%D 2020
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Otto Mutzbauer; Elias Toubassi; Andrija Vodopivec. Quasibases for nonseparable $p$-groups. Rendiconti del Seminario Matematico della Università di Padova, Tome 144 (2020), pp. 197-215. doi : 10.4171/rsmup/65. http://www.numdam.org/articles/10.4171/rsmup/65/

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