Geodesic
On self-maps which induce identity automorphisms of homology groups
Glasgow mathematical journal, Tome 43 (2001) no. 2, pp. 177-184

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We derive a finite normal series for the group {\rm Aut}\nolimits _*(X\;\!) of self-homotopy equivalences which induce identity automorphisms of homology groups, where X is a countable, simply-connected and finite-dimensional CW-complex. 
Pavešić, Petar. On self-maps which induce identity automorphisms of homology groups. Glasgow mathematical journal, Tome 43 (2001) no. 2, pp. 177-184. doi: 10.1017/S0017089501020031
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     title = {On self-maps which induce identity automorphisms of homology groups},
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     year = {2001},
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     doi = {10.1017/S0017089501020031},
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