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Benjamin Steinberg
Benjamin Steinberg
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Conjecture: Let $p$ be a prime. Then the group   

$G := \langle a, b \ | \ a^2, b^3, (ab)^7, [a,b]^9, (([a,b]^4)b)^{2p} \rangle$ has

has a composition series of the form ${\rm PSL}(2,8) - {\rm Z}_p - {\rm Z}_p - {\rm Z}_p - {\rm Z}_p - {\rm Z}_p - {\rm Z}_p - {\rm Z}_p$.

Is there any literature on this subject, and if not, how can this conjecture be proved?

Conjecture: Let $p$ be a prime. Then the group  $G := \langle a, b \ | \ a^2, b^3, (ab)^7, [a,b]^9, (([a,b]^4)b)^{2p} \rangle$ has a composition series of the form ${\rm PSL}(2,8) - {\rm Z}_p - {\rm Z}_p - {\rm Z}_p - {\rm Z}_p - {\rm Z}_p - {\rm Z}_p - {\rm Z}_p$.

Is there any literature on this subject, and if not, how can this conjecture be proved?

Conjecture: Let $p$ be a prime. Then the group 

$G := \langle a, b \ | \ a^2, b^3, (ab)^7, [a,b]^9, (([a,b]^4)b)^{2p} \rangle$

has a composition series of the form ${\rm PSL}(2,8) - {\rm Z}_p - {\rm Z}_p - {\rm Z}_p - {\rm Z}_p - {\rm Z}_p - {\rm Z}_p - {\rm Z}_p$.

Is there any literature on this subject, and if not, how can this conjecture be proved?

Tried to improve the formulation of the question.
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Stefan Kohl ♦
Stefan Kohl ♦
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My conjecture is that the groups (a,b|a^2, b^3,Conjecture: Let (ab)^7, [a,b]^9,$p$ be a prime. Then the group (([a,b]^4)b)^2p)) have$G := \langle a, b \ | \ a^2, b^3, (ab)^7, [a,b]^9, (([a,b]^4)b)^{2p} \rangle$ has a composition series: of the form PSL(2,8)-Z(p)-Z(p)-Z(p)-Z(p)-Z(p)-Z(p)-Z(p)${\rm PSL}(2,8) - {\rm Z}_p - {\rm Z}_p - {\rm Z}_p - {\rm Z}_p - {\rm Z}_p - {\rm Z}_p - {\rm Z}_p$. 

Is there any literature on this subject, and if not, how do I prove thecan this conjecture be proved?

My conjecture is that the groups (a,b|a^2, b^3, (ab)^7, [a,b]^9, (([a,b]^4)b)^2p)) have a composition series: PSL(2,8)-Z(p)-Z(p)-Z(p)-Z(p)-Z(p)-Z(p)-Z(p). Is there any literature on this subject, and if not, how do I prove the conjecture?

Conjecture: Let $p$ be a prime. Then the group $G := \langle a, b \ | \ a^2, b^3, (ab)^7, [a,b]^9, (([a,b]^4)b)^{2p} \rangle$ has a composition series of the form ${\rm PSL}(2,8) - {\rm Z}_p - {\rm Z}_p - {\rm Z}_p - {\rm Z}_p - {\rm Z}_p - {\rm Z}_p - {\rm Z}_p$. 

Is there any literature on this subject, and if not, how can this conjecture be proved?

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Thomas
Thomas
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Group theory conjecture on hurwitz groups

My conjecture is that the groups (a,b|a^2, b^3, (ab)^7, [a,b]^9, (([a,b]^4)b)^2p)) have a composition series: PSL(2,8)-Z(p)-Z(p)-Z(p)-Z(p)-Z(p)-Z(p)-Z(p). Is there any literature on this subject, and if not, how do I prove the conjecture?