Related papers: A mixed version for a Fuchs' Lemma

A classical theorem of Frucht states that any finite group appears as the automorphism group of a finite graph. In the quantum setting the problem is to understand the structure of the compact quantum groups which can appear as quantum…

It is shown that any finitely generated non-elementary Fuchsian group has among its homomorphic images all but finitely many of the alternating groups. This settles in the affirmative a conjecture of Graham Higman.

The additivity with respect to exact sequences is notoriously a fundamental property of the algebraic entropy of group endomorphisms. It was proved for abelian groups by deeply exploiting their structure. On the other hand, a solvable…

Many results have been established that show how the number of conjugacy classes appearing in the product of classes affect the structure of a finite group. The aim of this paper is to show several results about solvability concerning the…

In this paper we prove that $\ell$-group tensor product of archimedean $f$-rings is an $f$-ring. We will use this result to characterize multiplicative $\ell$-bimorphisms between unital $f$-rings.

Euler's Gamma function $\Gamma$ either increases or decreases on intervals between two consequtive critical points. The inverse of $\Gamma$ on intervals of increase is shown to have an extension to a Pick-function and similar results are…

Chevalley's theorem and it's converse, the Sheppard-Todd theorem, assert that finite reflection groups are distinguished by the fact that the ring of invariant polynomials is freely generated. We show that in the Euclidean case, a weaker…

Aiming at a better understanding of finite groups as finite dynamical systems, we show that by a version of Fitting's Lemma for groups, each state space of an endomorphism of a finite group is a graph tensor product of a finite directed…

We prove a version of Grothendieck's descent theorem on an `enriched' principal fiber bundle, a principal fiber bundle with an action of a larger group scheme. Using this, we prove the isomorphisms of the equivariant Picard and the class…

We present an overview of the close analogies between the character rings of finite groups and the fusion rings of rational conformal models, which follow from general principles related to orbifold deconstruction.

We construct the augmentation representation. It is a representation of the fundamental group of the link complement associated to an augmentation of the framed cord algebra. This construction connects representations of two link invariants…

Based on a bijection due to Fu and Tang, we provide combinatorial proofs of several partition identities of Andrews and Merca. We also introduce two weights for partitions to extend one of these identities.

In this paper, we classify finite categories with two objects such that one of the endomorphism monoids is a group. We prove that having a group on one side affects the structure of the other endomorphism monoid, and we prove that it is…

In this paper we use automorph class theory formalism to construct a lifting of similitudes of quadratic Z-modules of arbitrary ternary nondegenerate quadratic forms to morphisms between certain subrings of associated Clifford algebras. The…

We construct a commutative version of the group ring and show that it allows one to translate questions about the normal generation of groups into questions about the generation of ideals in commutative rings. We demonstrate this with an…

We give a proof of the geometric fundamental lemma of Kottwitz. As explained by Laumon, this implies the fundamental lemma for the unitary groups.

We prove that the finitely presentable subgroups of residually free groups are separable and that the subgroups of type $\mathrm{FP}_\infty$ are virtual retracts. We describe a uniform solution to the membership problem for finitely…

We show that the ring of multisymmetric functions over a commutative ring is isomorphic to the ring generated by the coefficients of the characteristic polynomial of polynomials in commuting generic matrices. As a consequence we give a…

Let B be a unital C*-algebra, let A be a unital subalgebra, and let E be a conditional expectation from B to A with index-finite type and a quasi-basis of n elements. Then the topological stable rank satisfies \tsr (B) \leq \tsr (A) + n -…

A decomposition theorem for the Lind zeta function of a reversal system $(X, T, R)$ of finite order is established. A reversal system can be regarded as an action of a certain group $G$ on $X$. To establish an explicit formula for the Lind…