PSL(2,p) satisfies the replacement property exactly for p in {7,11,19,31} and p congruent to 3 or -3 modulo both 8 and 10; however, the proof of the failure cases contains a false construction.
Finite soluble groups satisfying the replacement property
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abstract
We investigate the finite soluble groups $G$ with the following property (replacement property): for every irredundant generating set $\{g_1,\dots,g_m\}$ of maximal size and for any $1\neq g\in G$ there exists an $i\in \{1,\dots,m\}$ so that $\langle g_1,\dots,g_{i-1},g,g_{i+1},\dots,g_m\rangle=G.$
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math.GR 1years
2019 1verdicts
REJECT 1representative citing papers
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On the Replacement Property for PSL(2, p)
PSL(2,p) satisfies the replacement property exactly for p in {7,11,19,31} and p congruent to 3 or -3 modulo both 8 and 10; however, the proof of the failure cases contains a false construction.