Let G be a finite p-group and let F be the field of p elements. It is shown that if G is elementary abelian-by-cyclic then the isomorphism type of G is determined by FG.
@article{bwmeta1.element.bwnjournal-article-cmv82i1p125bwm, author = {Czes\l aw Bagi\'nski}, title = {On the isomorphism problem for modular group algebras of elementary abelian-by-cyclic p-groups}, journal = {Colloquium Mathematicae}, volume = {79}, year = {1999}, pages = {125-136}, zbl = {0943.20007}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv82i1p125bwm} }
Bagiński, Czesław. On the isomorphism problem for modular group algebras of elementary abelian-by-cyclic p-groups. Colloquium Mathematicae, Tome 79 (1999) pp. 125-136. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv82i1p125bwm/
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