Pseudo-mitotic groups.

*(English)*Zbl 0569.20039The concept of a mitotic group was used by G. Baumslag, E. Dyer and A. Heller [J. Pure Appl. Algebra 16, 1-47 (1980; Zbl 0419.20026)] to prove results on embeddings of groups into acyclic groups. In the paper under review this concept is generalized to that of what is called a pseudo-mitotic group, and it is poved that pseudo-mitotic groups are acyclic. Since the group \(G_ n\) of homeomorphisms of \({\mathbb{R}}^ n\) with compact support is pseudo-mitotic but not known to be mitotic in this way a uniform proof for the acyclicity of all \(G_ n\)- which is actually due already to Mather - and of all mitotic groups is obtained. It is also shown that it is not possible to get functorial embeddings of groups into algebraically closed groups.

Reviewer: J.Huebschmann

##### MSC:

20J05 | Homological methods in group theory |

57S05 | Topological properties of groups of homeomorphisms or diffeomorphisms |

20F34 | Fundamental groups and their automorphisms (group-theoretic aspects) |

20F38 | Other groups related to topology or analysis |

20E06 | Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations |

20E07 | Subgroup theorems; subgroup growth |

##### Keywords:

embeddings of groups; acyclic groups; pseudo-mitotic groups; functorial embeddings; algebraically closed groups
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\textit{K. Varadarajan}, J. Pure Appl. Algebra 37, 205--213 (1985; Zbl 0569.20039)

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##### References:

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