Construction of some subgroups in black box groups ${\mathrm{PGL}}_2(q)$ and ${(\mathrm{P})\mathrm{SL}}_2(q)$

Abstract

For the black box groups $X$ encrypting ${\mathrm{PGL}}_2(q)$, $q$ odd, we propose an algorithm constructing a subgroup encrypting ${\mathrm{Sym}}_4$ and subfield subgroups of $X$. We also present the analogous algorithms for black box groups encrypting ${(\mathrm{P})\mathrm{SL}}_2(q)$.

arXiv admin note: text overlap with arXiv:1302.3059

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