Related papers: More Counterexamples to the Unit Conjecture for Gr…

We verify Curtis conjecture on a class of elements of ${_2\pi_*^s}$ that satisfy a certain factorisation property. To be more precise, suppose $f\in{_2\pi_n^s}$ pulls back to $g\in{_2\pi_n^s}P$ through the Kahn-Priddy map $\lambda:QP\to…

The article provides a counterexample to a conjecture by Blocki-Zwonek.

Another counter-example to Dirac's Conjecture is presented, which resembles the Cawley model but is so modified as to include second class constraints. The arbitrary function in the general solution to the defining equations of momenta…

We prove that for any prime $p>2$, $q=p^\nu$ a power of $p$, $n\ge p$ and $G=S_n$ or $G=A_n$ (symmetric or alternating group) there exists a Galois extension $K/\mathbb F_q(T)$ ramified only over $\infty$ with $\mathrm{Gal}(K/\mathbb…

We introduce structure theorems for the study of the unit conjecture for supersoluble group rings and apply our results to the (Passman) fours group G. We show that over any field K, the group algebra KG has no non-trivial units of length…

We consider the Zassenhaus conjecture for the normalized unit group of the integral group ring of the Mathieu sporadic group M12. As a consequence, we confirm for this group the Kimmerle's conjecture on prime graphs.

We consider the capability of $p$ groups of class two and odd prime exponent. We use linear algebra and counting arguments to establish a number of new results. In particular, we settle the 4-generator case, and prove a sufficient condition…

We establish a number of "concatenation theorems" that assert, roughly speaking, that if a function exhibits "polynomial" (or "Gowers anti-uniform", "uniformly almost periodic", or "nilsequence") behaviour in two different directions…

Reduced power series in two variables with coefficients in a field of characteristic zero satisfy a well-known formula that relates a codimension related to the normalization of a ring and the jacobian ideal. In the general case Deligne…

It is shown that in the units of augmentation one of an integral group ring $\mathbb{Z} G$ of a finite group $G$, a noncyclic subgroup of order $p^{2}$, for some odd prime $p$, exists only if such a subgroup exists in $G$. The corresponding…

We prove a GL(n)xGL(n-1) local converse theorem for l-adic families of smooth representations of GL(n,F) where F is a finite extension of Q_p and l is different from p. To do so, we also extend the theory of Rankin-Selberg integrals, first…

Zagier provided eleven conjectural rank two examples for Nahm's problem. All of them have been proved in the literature except for the fifth example, and there is no $q$-series proof for the tenth example. We prove that the fifth and the…

By creating a new method, the author proved the well-known world's baffling problems Goldbach conjecture, twin primes conjecture, the Proposition (C) and the Proposition $n^2+1$.

Let G be any abelian group and {a_sG_s}_{s=1}^k be a finite system of cosets of subgroups G_1,...,G_k. We show that if {a_sG_s}_{s=1}^k covers all the elements of G at least m times with the coset a_tG_t irredundant then [G:G_t]\le 2^{k-m}…

We consider non-trivial irreducible tensor products of modular representations of a symmetric group $S_n$ in characteristic 2 for even $n$ completing the proof of a classification conjecture of Gow and Kleshchev about such products.

We prove some anologues for algebras of recent group-theoretic results (due to Khukhro, Klyachko, Makarenko, Milentyeva, and Shumyatsky) on large characteristic subgroups satisfying a given property.

In this article we present the history of auxiliary primes used in proofs of reciprocity laws from the quadratic to Artin's reciprocity law. We also show that the gap in Legendre's proof can be closed with a simple application of Gauss's…

We expand on two existing characterizations of rings of Gorenstein (weak) global dimension zero and give two new characterizations of rings of finite Gorenstein (weak) global dimension. We also include the answer to a question of Y.~Xiang…

This paper establishes the correctness of a conjecture of Bertram-Feinberg and Mukai for a special class of globally generated rank-two bundles with canonical determinant over a generic Riemann surface of genus at least four.

King's conjecture states that on every smooth complete toric variety $X$ there exists a strongly exceptional collection which generates the bounded derived category of $X$ and which consists of line bundles. We give a counterexample to this…