The order of the non-abelian tensor product of groups
Let $G$ and $H$ be groups that act compatibly on each other. We denote by $[G,H]$ the derivative subgroup of $G$ under $H$. We prove that if the set $\{g^{-1}g^h \mid g \in G, h \in H\}$ has $m$ elements, then the derivative $[G,H]$ is finite with $m$-bounded order. Moreover, we show that if the set...
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Main Authors | , , |
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Format | Journal Article |
Language | English |
Published |
11.12.2018
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Subjects | |
Online Access | Get full text |
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Summary: | Let $G$ and $H$ be groups that act compatibly on each other. We denote by
$[G,H]$ the derivative subgroup of $G$ under $H$. We prove that if the set
$\{g^{-1}g^h \mid g \in G, h \in H\}$ has $m$ elements, then the derivative
$[G,H]$ is finite with $m$-bounded order. Moreover, we show that if the set of
all tensors $T_{\otimes}(G,H) = \{g\otimes h \mid g \in G, h\in H\}$ has $m$
elements, then the non-abelian tensor product $G \otimes H$ is finite with
$m$-bounded order. We also examine some finiteness conditions for the
non-abelian tensor square of groups. |
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DOI: | 10.48550/arxiv.1812.04747 |