Related papers: Donovan's conjecture and blocks with abelian defec…

For a group G relatively hyperbolic to a family of residually finite groups satisfying the Farrell-Jones conjecture, we reduce the solution of the Farrell-Jones conjecture for G to the case of certain nice cyclic extensions in G.

We prove the Burghelea Conjecture for groups satisfying some additional cohomological property.

A special case of a conjecture raised by Forrest and Runde (Math. Zeit., 2005) asserts that the Fourier algebra of every non-abelian connected Lie group fails to be weakly amenable; this was aleady known to hold in the non-abelian compact…

We prove analogues for reductive algebraic groups of some results for finite groups due to Knoerr and Robinson which play a central role in their reformulation of Alperin's conjecture for finite groups.

In this article we formulate a version of the analytic Novikov conjecture for semigroups rather than groups, and show that the descent argument from coarse geometry generalises effectively to this new situation.

We show that complex semisimple quantum groups, that is, Drinfeld doubles of $ q $-deformations of compact semisimple Lie groups, satisfy a categorical version of the Baum-Connes conjecture with trivial coefficients. This approach, based on…

A famous conjecture attributed to Dardano-Dikranjan-Rinauro-Salce states that any uniformly fully inert subgroup of a given group is commensurable with a fully invariant subgroup (see, respectively, [5] and [6]). In this short note, we…

The conjecture that semi-p-abelian groups is strongly semi-p-abelian is flase for p=3.And it's true for metabelian semi-p-abelian groups.

Recently, Moret\'o and Rizo proposed a conjecture, known as the Picky Conjecture, proposing new character correspondences extending the McKay Conjecture. We prove the Picky Conjecture for all quasi-simple groups of Lie type for non-defining…

We determine the numerical invariants of blocks with defect group D_{2^n} * C_{2^m} = Q_{2^n} * C_{2^m} (central product), where n > 2 and m > 1. As a consequence, we prove Brauer's k(B)-conjecture, Olsson's conjecture (and more generally…

The longstanding Alperin weight conjecture and its blockwise version have been reduced to simple groups recently by Navarro, Tiep, Spaeth and Koshitani. Thus, to prove this conjecture, it suffices to verify the corresponding inductive…

Following Craven and Rouquier's computational method to tackle Brou\'e's abelian defect group conjecture, we present two algorithms implementing that procedure in the case of principal blocks of defect $D \cong C_{\ell} \times C_{\ell}$ for…

We prove that negative K-groups of small abelian categories are trivial.

We formulate and prove Chevalley's theorem in the setting of affine Nash groups. As a consequence, we show that the semi-direct product of two almost linear Nash groups is still an almost linear Nash group.

We prove that Sp\"ath's Character Triple Conjecture holds for every finite group with respect to maximal defect characters at the prime 2. This is done by reducing the maximal defect case of the conjecture to the so-called inductive…

We classify the Morita equivalence classes of blocks with elementary abelian defect groups of order $16$ with respect to a complete discrete valuation ring with algebraically closed residue field of characteristic two. As a consequence,…

We prove that Brauer's Height Zero Conjecture holds for p-blocks of finite groups with metacyclic defect groups. If the defect group is nonabelian and contains a cyclic maximal subgroup, we obtain the distribution into p-conjugate and…

We calculate examples of Picard groups for 2-blocks with abelian defect groups with respect to a complete discrete valuation ring. These include all blocks with abelian 2-groups of 2-rank at most three with the exception of the principal…

We show an invariance result for the L2-torsion of groups under uniform measure equivalence provided a measure-theoretic version of the determinant conjecture holds. The measure-theoretic determinant conjecture is discussed and, for…

The study of Fuglede's conjecture on the direct product of elementary abelian groups was initiated by Iosevich et al. For the product of two elementary abelian groups the conjecture holds. For $\mathbb{Z}_p^3$ the problem is still open if…