Let $p>2$ be a prime, $C_p$ be the additive group of integers mod $p$. Then the multiplicative group $\{1,...,p1\}$ of units in the field $Z/pZ$ is cyclic of order $p1$, it acts on $C_p$ by left multiplication. Let $G_p$ be the corresponding semidirect product of order $p(p1)$. Question: does this group admit a presentation with 2 defining relations for some (all) $p > 3$? For $p=3$, $G_p$ is the symmetric group $S_3$ and it admits the balanced presentation $\langle a,b \mid a^2=1, aba=b^2\rangle$. (The question is attributed to Alex Lubotzky.) For example, what if $p=5$? Does $G_5$, a cyclicbycyclic group of order 20, admit a presentation with 2 generators and 2 defining relations?
G_{5} has a presentation on generators a,b and relations ba=aab, abbabb=1. 


Martin Kassabov informed me that http://front.math.ucdavis.edu/0804.1396 contains the fact for all $p$ (see Example 3.5 (2) on page 7). The presentation was discovered by B. Neumann in 1956. 

