arXiv subjects
Publications and source records attributed to Erzsébet Horváth.
For a subgroup $H$ of a finite group $G$, the Frobenius graph $Γ(G, H)$ records the constituents of the restrictions to $H$ of the irreducible characters of $G$. We investigate when this graph has diameter 3.
In Part I of this paper, we introduced a class of certain algebras of finite dimension over a field. All these algebras are split, symmetric and local. Here we continue to investigate their Loewy structure. We show that in many cases their Loewy length is equal to an upper bound established in Part I, but we also construct examples where we have a strict inequality.
We determine the combinatorial and the ordinary depth of the maximal subgroups of the simple Ree groups, $R(q)$.
The Sylow p-subgroups of the symmetric group S_p^n satisfy the appropriate generalization of Maschke's Theorem to the case of a p'-group acting on a (not necessarily abelian) p-group. Moreover, some known results about the Sylow p-subgroups of S_p^n are stated in a form that is true for all primes p.
We determine the combinatorial depth of certain subgroups of simple Suzuki groups Sz(q), among others the depth of their maximal subgroups. We apply these results to determine the ordinary depth of these subgroups.