Abstract
AbstractWe prove that the minimal representation dimension of a direct product G of non-abelian groups $$G_1,\ldots ,G_n$$
G
1
,
…
,
G
n
is bounded below by $$n+1$$
n
+
1
and thereby answer a question of Abért. If each $$G_i$$
G
i
is moreover non-solvable, then this lower bound can be improved to be 2n. By combining this with results of Pyber, Segal, and Shusterman on the structure of boundedly generated groups, we show that branch groups cannot be boundedly generated.
Publisher
Springer Science and Business Media LLC
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