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Search: MSC category 20F28 ( Automorphism groups of groups [See also 20E36] )

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1. CMB 2007 (vol 50 pp. 206)

Golasiński, Marek; Gonçalves, Daciberg Lima
Spherical Space Forms: Homotopy Types and Self-Equivalences for the Group $({\mathbb Z}/a\rtimes{\mathbb Z}/b) \times SL_2\,(\mathbb{F}_p)$
Let $G=({\mathbb Z}/a\rtimes{\mathbb Z}/b) \times \SL_2(\mathbb{F}_p)$, and let $X(n)$ be an $n$-dimensional $CW$-complex of the homotopy type of an $n$-sphere. We study the automorphism group $\Aut (G)$ in order to compute the number of distinct homotopy types of spherical space forms with respect to free and cellular $G$-actions on all $CW$-complexes $X(2dn-1)$, where $2d$ is the period of $G$. The groups ${\mathcal E}(X(2dn-1)/\mu)$ of self homotopy equivalences of space forms $X(2dn-1)/\mu$ associated with free and cellular $G$-actions $\mu$ on $X(2dn-1)$ are determined as well.

Keywords:automorphism group, $CW$-complex, free and cellular $G$-action, group of self homotopy equivalences, Lyndon--Hochschild--Serre spectral sequence, special (linear) group, spherical space form
Categories:55M35, 55P15, 20E22, 20F28, 57S17

2. CMB 1998 (vol 41 pp. 98)

Papistas, Athanassios I.
Automorphisms of metabelian groups
We investigate the problem of determining when $\IA (F_{n}({\bf A}_{m}{\bf A}))$ is finitely generated for all $n$ and $m$, with $n\geq 2$ and $m\neq 1$. If $m$ is a nonsquare free integer then $\IA(F_{n}({\bf A}_{m}{\bf A}))$ is not finitely generated for all $n$ and if $m$ is a square free integer then $\IA(F_{n}({\bf A}_{m}{\bf A}))$ is finitely generated for all $n$, with $n\neq 3$, and $\IA(F_{3}({\bf A}_{m}{\bf A}))$ is not finitely generated. In case $m$ is square free, Bachmuth and Mochizuki claimed in ([7], Problem 4) that $\TR({\bf A}_{m}{\bf A})$ is $1$ or $4$. We correct their assertion by proving that $\TR({\bf A}_{m}{\bf A})=\infty $.


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