I came across this article (Bender, P. "Eine Präsentation der symplektischen Gruppe $\mathrm{Sp}(4,\mathbb{Z})$ mit 2 Erzeugenden und 8 definierenden Relationen" 
[“Presentation of Symplectic Group $\mathrm{Sp}(4,\mathbb{Z})$ with 2 Generatrices and 8 Definitive Relations.”] Journal of Algebra **65**, no. 2 (1980): 328-331)


The paper seems like a lot of computation without much motivation. I am just curious to know if any one can tell me the motivation to consider these underlined words? Do they have any special meaning in the symplectic group. Or is it just brute force computation? 



Presentation of $\mathrm{Sp}(4, \mathbb{Z})$
Presentations for the Siegel modular groups $Sp(2g,\mathbb{Z})$ are closely related to presentations of the surface mapping class group.In general, the braid group $B\_{2g+2}$
acts on the free group $F\_{2g}$, inducing a homomorphism from $B\_{2g+2}$ into $Sp(2g,\mathbb{Z})$. For $g=2$, Kassel has shown that the latter homomorphism is surjective 
and has determined its kernel (thus obtaining a braid-type presentation of $Sp(4,\mathbb{Z})$).
The article discusses how exactly Behr's presentation and Bender's slightly shortened presentation can be interpreted this way. The link is:arxiv.org/pdf/1204.2377, and there
Theorem $4.3$ and its proof.
I hope this helps.


