We partially prove and partially disprove Oka’s conjecture on the fundamental group/Alexander polynomial of an irreducible plane sextic. Among other results, we enumerate all irreducible sextics with simple singularities admitting dihedral coverings and find examples of Alexander equivalent Zariski pairs of irreducible

Let S be a compact surface with empty boundary. A classical result from the 1920s by Tibor Radó asserts that every compact surface with empty boundary (usually called a closed surface) admits a triangulation [1]. Let e be any edge of a triangulation T of S . The contraction of e in T consists of contracting e to a single vertex and collapsing each of the two triangles meeting e into a single ed...

in this paper, we introduce and study the prime, strongly prime,semiprime and irreducible fuzzy bi-ideals of a semigroup. we characterize thosesemigroups for which each fuzzy bi-ideal is semiprime. we also characterizethose semigroups for which each fuzzy bi-ideal is strongly prime.

let $g$ be a finite group and let $text{cd}(g)$ be the set of all‎ ‎complex irreducible character degrees of $g$‎. ‎b‎. ‎huppert conjectured‎ ‎that if $h$ is a finite nonabelian simple group such that‎ ‎$text{cd}(g) =text{cd}(h)$‎, ‎then $gcong h times a$‎, ‎where $a$ is‎ ‎an abelian group‎. ‎in this paper‎, ‎we verify the conjecture for‎ ‎${f_4(2)}.$‎

In this article we initiate a systematic study of irreducible weight modules over direct limits of reductive Lie algebras, and in particular over the simple Lie algebras A(∞), B(∞), C(∞) and D(∞). Our main tool is the shadow method introduced recently in [DMP]. The integrable irreducible modules are an important particular class and we give an explicit parametrization of the finite integrable m...

We describe an algorithm for explicitly listing the irreducible monomial subgroups of GL(n, q) , given a suitable list of finite irreducible monomial subgroups of GL(n, C) , where n is 4 or a prime, and q is a prime power. Particular attention is paid to the case n = 4, and the algorithm is illustrated for n = 4 and q = 5. Certain primitive permutation groups can be constructed from a list of i...

A theorem of William Jaco and Eric Sedgwick states that if M is an irreducible, ∂-irreducible 3-manifold with boundary a single torus, and if M contains no genus one essential (incompressible and ∂-incompressible) surfaces, then M cannot contain infinitely many distinct isotopy classes of essential surfaces of uniformly bounded genus. The main result in this paper is a generalization: If M is a...

By utilizing an irreducible inclusion of type IIIq2 factors coming from a free-product type action of the quantum group SUq(2), we show that the free group factor L(F∞) possesses irreducible subfactors of arbitrary index > 4. Combined with earlier results of Radulescu, this shows that L(F∞) has irreducible subfactors with any index value in {4 cos(π/n) : n ≥ 3} ∪ [4,+∞).

We call a pseudovariety finite join irreducible if V ≤ V1 ∨V2 =⇒ V ≤ V1 or V ≤ V2. We present a large class of group mapping semigroups generating finite join irreducible pseudovarieties. We show that many naturally occurring pseudovarieties are finite join irreducible including: S, DS, CR, CS and H, where H is a group pseudovariety containing a non-nilpotent group.

Founding harmonic analysis on classical simple complex groups, I.M. Gelfand and M.A. Naimark in their classical book [GN] posed three basic questions: unitary duals, characters of irreducible unitary representations and Plancherel measures. In the case of reductive p-adic groups, the only series of reductive groups where unitary duals are known are general linear groups. In this paper we reduce...