Related papers: On multivalued groups of order 3

In the note we prove that all composition factors of a finite group possessing a Carter subgroup of odd order either are abelain, or are isomorphic to $L_2(3^{2n+1})$.

Explicit bases for the spaces of holomorphic cusp forms of all even positive weights and all orders are constructed. The dimensions of these spaces are computed.

The finite groups having an indecomposable polynomial invariant whose degree is at least half of the order of the group are classified. Apart from four sporadic exceptions these are exactly the groups having a cyclic subgroup of index at…

The classification of elliptic curves E over the rationals Q is studied according to their torsion subgroups E_{tors}(Q) of rational points. Explicit criteria for the classification are given when E_{tors}(Q) are cyclic groups with even…

We consider the coset poset associated with the families of proper subgroups, proper subgroups of finite index, and proper normal subgroups of finite index. We investigate under which conditions those coset posets have contractible…

It is proved that finite nonabelian simple groups $S$ with $\max \pi(S)=37$ are uniquely determined by their order and degree pattern in the class of all finite groups.

We show that every bipartite planar graph with minimum degree at least 3 has proper orientation number at most 3.

Rank-2 and rank-3 tensors are almost all identifiable with only few exceptions. We classify them all together with the dimensions and the structures of all the sets evincing the rank.

We obtain a complete classification of complex-valued sequences which are both multiplicative and automatic.

We determine the $3$-class groups of $\mathbb{Q}(\sqrt[3]{p})$ and $K=\mathbb{Q}(\sqrt[3]{p},\sqrt{-3})$ when $p\equiv 4,7\bmod 9$ is a prime and $3$ is a cubic modulo $p$. This confirms a conjecture made by Barrucand-Cohn, and proves the…

In this note we give a classification of the Maximal order Abelian subgroups of finite irreducible Coxeter groups. We also prove a Weyl group analogue of Cartan's theorem that all maximal tori in a connected compact Lie group are conjugate.

For a perfect field $k$, we construct a triangulated category of mixed motives over $k[t]/{(t^{m+1})}$. The ext groups in this category are given by higher Chow groups, and additive higher Chow groups.

We classify all finite groups with five relative commutativity degrees. Also, we give a partial answer to our previous conjecture on a lower bound of the number of relative commutativity degrees of finite groups.

In this extended abstract we announce a proof that, in a Coxeter group of rank 3, low elements are in bijection with small inversion sets. This gives a partial confirmation of Conjecture 2 in [Dyer, Hohlweg '16]. That same article provides…

We compute the integral third homology of most of the sporadic finite simple groups and of their central extensions.

In this article, we prove that every finite abelian group $G$ of odd order occurs as a subgroup of the class group of infinitely many real cyclotomic fields.

We prove rationality of the moduli variety of curves of genus 3.

We give a classification and a construction of all smooth $(n-1)$-dimensional varieties of lines in ${\bf P}\sp n$ verifying that all their lines meet a curve. This also gives a complete classification of $(n-1)$-scrolls over a curve…

We give a complete classification of complex hyperbolic $(n_1, n_2, n_3)$-triangle groups by types defined according to the ellipticity of two particular words of short length. This improves the Schwartz conjecture proved by Grossi.

The article contains some important classes of multisets. Combinatorial proofs of problems on the number of m-submultisets and m-permutations of multiset elements are considered and effective algorithms for their calculation are given. In…