Among the six classes of pro-2-groups of finite and fixed co-classes and trivial Schur Multiplicator which studied by Abdolzadeh and Eick in 2009, there are two classes $$S_5=langle a,bmid [b,a^2]=1, a^2=[b,a]^2, (b^2)^{[b,a]}b^2=1rangle$$ and $$S_6=langle a,t,bmid a^2=b^2,[b,a]^2=1, t^a=t^{-1}[b,a], b^t=abarangle$$that have been conjectured to have deficiency zero presentations. In this paper we prove these conjectures. This completes the efficiency of all six classes of pro-$2$-groups of fixed co-classes.
Arjomandfar, A., & Doostie, H. (2011). Proving the efficiency of pro-2-groups of fixed co-classes. Bulletin of the Iranian Mathematical Society, 37(No. 4), 73-80.
MLA
A. Arjomandfar; H. Doostie. "Proving the efficiency of pro-2-groups of fixed co-classes". Bulletin of the Iranian Mathematical Society, 37, No. 4, 2011, 73-80.
HARVARD
Arjomandfar, A., Doostie, H. (2011). 'Proving the efficiency of pro-2-groups of fixed co-classes', Bulletin of the Iranian Mathematical Society, 37(No. 4), pp. 73-80.
VANCOUVER
Arjomandfar, A., Doostie, H. Proving the efficiency of pro-2-groups of fixed co-classes. Bulletin of the Iranian Mathematical Society, 2011; 37(No. 4): 73-80.