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Yiftach Barnea
Yiftach Barnea
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We are looking for examples of groups $G$ such that $G$ is "big", but $Out(G)$ is trivial. By "big" we mean things like virtually free, or large, or Golod-Shafarevich. However, we would like our groups to be residually-finite.

Edit: Henry, Igor and Lee thank you for all your help. Eventually, we only needed finite $Out(G)$ with $G$ having a trivial center. Thus, $A*B$ was the example we used. It is included in "Large normal subgroup growth and large characteristic subgroup growth" (sorry for the self-promotion, but I thought people might be interested in our motivation and the results of their help).

We are looking for examples of groups $G$ such that $G$ is "big", but $Out(G)$ is trivial. By "big" we mean things like virtually free, or large, or Golod-Shafarevich. However, we would like our groups to be residually-finite.

Edit: Henry, Igor and Lee thank you for all your help. Eventually, we only needed finite $Out(G)$ with $G$ having trivial center. Thus, $A*B$ was the example we used. It is included in "Large normal subgroup growth and large characteristic subgroup growth" (sorry for the self-promotion, but I thought people might be interested in our motivation and the results of their help).

We are looking for examples of groups $G$ such that $G$ is "big", but $Out(G)$ is trivial. By "big" we mean things like virtually free, or large, or Golod-Shafarevich. However, we would like our groups to be residually-finite.

Edit: Henry, Igor and Lee thank you for all your help. Eventually, we only needed finite $Out(G)$ with $G$ having a trivial center. Thus, $A*B$ was the example we used. It is included in "Large normal subgroup growth and large characteristic subgroup growth" (sorry for the self-promotion, but I thought people might be interested in our motivation and the results of their help).

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Source Link
Yiftach Barnea
Yiftach Barnea
  • 5.5k
  • 2
  • 38
  • 53

We are looking for examples of groups $G$ such that $G$ is "big", but $Out(G)$ is trivial. By "big" we mean things like virtually free, or large, or Golod-Shafarevich. However, we would like our groups to be residually-finite.

Edit: Henry, Igor and Lee thank you for all your help. Eventually, we only needed finite $Out(G)$ with $G$ having trivial center. Thus, $A*B$ was the example we used. It is included in "Large normal subgroup growth and large characteristic subgroup growth" (sorry for the self-promotion, but I thought people might be interested in our motivation and the results of their help).

We are looking for examples of groups $G$ such that $G$ is "big", but $Out(G)$ is trivial. By "big" we mean things like virtually free, or large, or Golod-Shafarevich. However, we would like our groups to be residually-finite.

We are looking for examples of groups $G$ such that $G$ is "big", but $Out(G)$ is trivial. By "big" we mean things like virtually free, or large, or Golod-Shafarevich. However, we would like our groups to be residually-finite.

Edit: Henry, Igor and Lee thank you for all your help. Eventually, we only needed finite $Out(G)$ with $G$ having trivial center. Thus, $A*B$ was the example we used. It is included in "Large normal subgroup growth and large characteristic subgroup growth" (sorry for the self-promotion, but I thought people might be interested in our motivation and the results of their help).

Source Link
Yiftach Barnea
Yiftach Barnea
  • 5.5k
  • 2
  • 38
  • 53

"Big" groups $G$ with trivial $Out(G)$

We are looking for examples of groups $G$ such that $G$ is "big", but $Out(G)$ is trivial. By "big" we mean things like virtually free, or large, or Golod-Shafarevich. However, we would like our groups to be residually-finite.