arXiv subjects

Daniel Appel

Publications and source records attributed to Daniel Appel.

3 recordsLinked to original sources

arXiv2010

On the Abelianization of Congruence Subgroups of Aut(F_2)

Let F_n be the free group of rank n and let Aut^+(F_n) be its special automorphism group. For an epimorphism pi : F_n -> G of the free group F_n onto a finite group G we call Gamma^+(G,pi) = {f in Aut^+(F_n) | pi*f = pi} the standard congruence subgroup of Aut^+(F_n) associated to G and pi. In the case n = 2 we fully describe the abelianization of Gamma^+(G,pi) for finite abelian groups G. Moreover, we show that if G is a finite non-perfect group, then Gamma^+(G,pi) < Aut^+(F_2) has infinite abelianization.

math.GR↗

arXiv2009

Regular Circulant Matrices

We consider the groups of regular circulant matrices over finite fields and integer residue class rings. In both cases we present a formula for the order of these groups. We also make a first step towards finding the algebraic structure of them.

math.CO↗

arXiv2008

On the Index of Congruence Subgroups of Aut(F_n)

For an epimorphism pi of the free group F_n onto a finite group G write Gamma(G,pi) for the group of all automorphisms f of F_n for which pi*f = pi. This is called the standard congruence subgroup of Aut(F_n) associated to G and pi. In the case n = 2 we present formulas for the index of Gamma(G,pi) where G is abelian or dihedral. Moreover, we show that congruence subgroups associated to dihedral groups provide a family of subgroups of arbitrary large index in Aut(F_2) generated by a fixed number of elements. This implies that finite index subgroups of Aut(F_2) cannot be written as free products.

math.GR↗