On the relationships between the factors of the upper and lower central series in some non-periodic groups

Dixon, Martyn; Kurdachenko, Leonid; Subbotin, Igor

doi:10.22108/ijgt.2017.21674

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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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On the relationships between the factors of the upper and lower central series in some non-periodic groups