arXiv subjects
Publications and source records attributed to Àngel García-Blázquez.
We prove that if two finite metacyclic groups have isomorphic rational group algebras, then they are isomorphic. This contributes to understand where is the line separating positive and negative solutions to the Isomorphism Problem for group algebras.
We prove that if $G$ and $H$ are finite metacyclic groups with isomorphic rational group algebras and one of them is nilpotent then $G$ and $H$ are isomorphic.
We obtain a new classification of the finite metacyclic group in terms of group invariants. We present an algorithm to compute these invariants, and hence to decide if two given finite metacyclic groups are isomorphic, and another algorithm which computes all the metacyclic groups of a given order. A GAP implementation of these algorithms is given.