Search Results

The gnu (or Group NUmber) function describes how many groups there are of a given order. The number of groups of each order are known up to 2047, see https://www.math.auckland.ac.nz/~obrien/research/g …

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 …

I was reading about the monster group, and how hard it was to do calculations in it, and I wondered: Is there a known presentation of the monster group? I know that it is a hurwitz group, but other th …

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 …

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 …

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 …

$\DeclareMathOperator\PSL{PSL}$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, …

Since the group $G := \langle a, b \ | \ a^2, b^3, (ab)^7, [a,b]^{10} \rangle$ seems to have resisted attacks of some powerful programs, I will turn to a group that seems to be a bit easier to analyse …

I'm trying to calculate a table of all simple hurwitz groups of order less than 10^7. None of the tables I found went further than 10^6, so I decided to use the tables of all simple groups up to 10^7 …

The Monster group is the largest of the sporadic simple groups, and has been proven by Wilson to also be a Hurwitz group. It has a presentation in terms of Coxeter groups, specifically Y443 along with …

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 …

My last question on the quotients of the group $$H := \langle a, b, c \ | \ a^2, b^2, c^2, (ab)^2, (ac)^3, (bc)^7, (abc)^{19} \rangle$$ couldn't be completely answered, because the finiteness of the g …

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 …

The paper An update on Hurwitz groups by Marston Conder seems to suggest that the Chevalley group $G(2,5)$ of order $5859000000$ is a quotient of $G := \langle a, b \ | \ a^2, b^3, (ab)^7, [a,b]^{10} …

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 …