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On the relationships between the factors of the upper and lower central series in some non-periodic groups | ||
International Journal of Group Theory | ||
مقاله 6، دوره 7، شماره 1، خرداد 2018، صفحه 37-50 اصل مقاله (231.05 K) | ||
نوع مقاله: Ischia Group Theory 2016 | ||
شناسه دیجیتال (DOI): 10.22108/ijgt.2017.21674 | ||
نویسندگان | ||
Martyn Dixon* 1؛ Leonid Kurdachenko2؛ Igor Subbotin3 | ||
1University of Alabama | ||
2National University of Dnepropetrovsk | ||
3National University | ||
چکیده | ||
This paper deals with the mutual relationships between the factor group $G/\zeta(G)$ (respectively $G/\zeta_k(G)$) and $G'$ (respectively $\gamma_{k+1}(G)$ and $G^{\mathfrak{N}}$). It is proved that if $G/\zeta(G)$ (respectively $G/\zeta_k(G)$) has finite $0$-rank, then $G'$ (respectively $\gamma_{k+1}(G)$ and $G^{\mathfrak{N}}$) also have finite $0$-rank. Furthermore, bounds for the $0$-ranks of $G', \gamma_{k+1}(G)$ and $G^{\mathfrak{N}}$ are obtained. | ||
کلیدواژهها | ||
finite rank؛ torsion-free rank؛ section $p$-rank؛ generalized radical group | ||
مراجع | ||
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