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I have found that $([a,b]^2[a,b^2])^n$ is a good relator to use in my search for quotients of $G := \langle a, b \ | \ a^2, b^3, (ab)^7, [a,b]^{10} \rangle$. For n<=5 $H := \langle a, b \ | \ a^2, b^3 …

I am currently working through all the groups with two generators, and I am up to the group with presentation $G := \langle a, b \ | \ a^2, b^3, (ab)^7, [a,b]^9 \rangle$. I have found all the finite q …

I've been thinking about quotients of groups, and I know that the abelianization G/[G,G] is important, but what about other quotients? Specifically, what about the quotient G/[G,[G,G]]? Is that import …

$\DeclareMathOperator\PSL{PSL}$I'm studying the Hurwitz group $(2, 3, 7; 9)$, with presentation: $G := \langle a, b \ | \ a^2, b^3, (ab)^7, [a,b]^9 \rangle$. This group has $\PSL_2(8)$ as a quotient, …

Sorry about asking so many questions, but I am a bit further on in my classification, and I am up to the group $G := \langle a, b \ | \ a^2, b^3, (ab)^7, [a,b]^{10}, ([a,b]^4b)^7 \rangle$. It has no s …

I was trying to find the free metabelian group of rank 2, and I realized that the wreath product of Z and Z is metabelian and has only 2 generators in its minimal generating set. I could not find a wa …

The only groups where 1/l+1/m+1/n is greater than one are the cyclic groups, the dihedral groups, and the groups A(4), S(4), and A(5). Therefore, A(5) is the only simple groups where 1/l+1/m+1/n>1. As …

Sorry about asking so many questions, but I had an idea for my study of groups, and I wanted to know if it was already a thing people use. My idea is to make a multiplication table with all the conjug …

I have been working with Hurwitz groups, and I came across the group $G := \langle a, b \ | \ a^2, b^3, (ab)^7, ([a,b]^2ab)^6 \rangle$. I'm trying to figure out exactly what this group is. I know it c …

In the question "Simple Hurwitz Groups of order less than 10^7", it came up that all the Hurwitz groups with absolutely irreducible projective representations of degrees up to 7 over any field are det …

It was shown that the only quotient of the group $G := \langle a, b \ | \ a^2, b^3, (ab)^7, [a,b]^{10} \rangle$ of the form PSL(2, q) is PSL(2, 41). That lead me to consider other families of simple g …

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 - {\r …

Since my question at Simplicity of infinite groups was not answered (well, at least, my second question), instead of trying to find the isomorhism type of those groups, I will instead try to find the …

I was experimenting with various presentations for groups, and I stumbled upon $G := \langle a, b \ | \ a^2, b^3, (ab)^7, [aba,b]^6 \rangle$. I found that it has order 11741184, but the magma calculat …

Actually, I just figured it out. The groups $H := \langle a, b \ | \ a^2, b^3, (ab)^7, [a,b]^{28}, [aba,b]^6 \rangle$ and $I := \langle a, b \ | \ a^2, b^3, (ab)^7, [a,b]^{8}, [aba,b]^6 \rangle$ are …