We will give an explicit description of non-commutative extensions over an ${\F}_p$-algebra of the additive group scheme (resp. the additive formal group scheme) by the group scheme (resp. the formal group scheme) which gives a deformation of the additive group scheme to the multiplicative group scheme (resp. the additive formal group scheme to the multiplicative formal group scheme).
@article{1176324096,
author = {Haraguchi, Yuki},
title = {On non-commutative extensions of $\widehat{\G}\_a$ by $\widehat{\Gg}^{(M)}$\\ over an ${\F}\_p$-algebra},
journal = {Hiroshima Math. J.},
volume = {37},
number = {1},
year = {2007},
pages = { 81-99},
language = {en},
url = {http://dml.mathdoc.fr/item/1176324096}
}
Haraguchi, Yuki. On non-commutative extensions of $\widehat{\G}_a$ by $\widehat{\Gg}^{(M)}$\\ over an ${\F}_p$-algebra. Hiroshima Math. J., Tome 37 (2007) no. 1, pp. 81-99. http://gdmltest.u-ga.fr/item/1176324096/