Geodesic
Direct Product Decompositions of Elation Groups
Canadian mathematical bulletin, Tome 20 (1977) no. 2, pp. 173-182

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Let G be a collineation group of a projective plane π. Let E be the subgroup generated by all elations in G. In the case that π is finite and G fixes no point or line, F. Piper [6; 7] has proved that if G contains certain combinations of perspectivities, then E is isomorphic to for some finite field g. 
Brown, Julia M. Nowlin. Direct Product Decompositions of Elation Groups. Canadian mathematical bulletin, Tome 20 (1977) no. 2, pp. 173-182. doi: 10.4153/CMB-1977-029-8
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     title = {Direct {Product} {Decompositions} of {Elation} {Groups}},
     journal = {Canadian mathematical bulletin},
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     year = {1977},
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     number = {2},
     doi = {10.4153/CMB-1977-029-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1977-029-8/}
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