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Automorphisms of the Gersten Group
Siberian Mathematical Journal ( IF 0.7 ) Pub Date : 2021-05-27 , DOI: 10.1134/s0037446621030046
F. A. Dudkin , E. A. Shaporina

The Gersten group \( G \) is the split extension \( F_{3}\rtimes_{\varphi}{𝕑} \) of the free group \( F_{3} \) with basis \( \{a,b,c\} \) by the automorphism \( \varphi:a\mapsto a,b\mapsto ba,c\mapsto ca^{2} \). We describe the generators and structure of the group \( \operatorname{Out}(G) \) and prove that \( \operatorname{Out}(G)\cong(F_{3}\times{𝕑}^{3})\rtimes({𝕑}_{2}\times{𝕑}_{2}) \).



中文翻译:

Gersten 群的自同构

Gersten 群\( G \)是自由群\( F_{3} \)的分裂扩展 \( F_{3}\rtimes_{\varphi}{𝕑} \)\( \{a,b ,c\} \)由自同构\( \varphi:a\mapsto a,b\mapsto ba,c\mapsto ca^{2} \)。我们描述了群的生成器和结构 \( \operatorname{Out}(G) \) 并证明 \( \operatorname{Out}(G)\cong(F_{3}\times{𝕑}^{3} )\rtimes({𝕑}_{2}\times{𝕑}_{2}) \) .

更新日期:2021-05-28
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