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- W2607368095 abstract "The maximal normal subgroup growth type of a finitely generated group is $n^{log n}$. Very little is known about groups with this type of growth. In particular, the following is a long standing problem: Let $Gamma$ be a group and $Delta$ a subgroup of finite index. Suppose $Delta$ has normal subgroup growth of type $n^{log n}$, does $Gamma$ has normal subgroup growth of type $n^{log n}$? We give a positive answer in some cases, generalizing a result of Muller and the second author and a result of Gerdau. For instance, suppose $G$ is a profinite group and $H$ an open subgroup of $G$. We show that if $H$ is a generalized Golod-Shafarevich group, then $G$ has normal subgroup growth of type of $n^{log n}$. We also use our methods to show that one can find a group with characteristic subgroup growth of type $n^{log n}$." @default.
- W2607368095 created "2017-04-28" @default.
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- W2607368095 date "2017-03-22" @default.
- W2607368095 modified "2023-09-23" @default.
- W2607368095 title "Large normal subgroup growth and large characteristic subgroup growth" @default.
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