Let n ⩾ 6 be an integer. We prove that the number of fields with Galois group A and absolute discriminant at most X is asymptotically least 1 / 8 + O ( ) . For , this improves upon previously best-known lower bound − 2 ! 4 ε due to Pierce, Turnage-Butterbaugh, Wood.

We first present a previously unpublished result of Stanton [11] that the group of order four generated by rotation by 90◦ acting on alternating sign matrices exhibits the CSP with the obvious q-analogue of |ASM(n)|. In [12], Wieland introduced a much larger cyclic group that acts on the set of alternating sign matrices. Unfortunately, it has a very complex orbit structure that does not exhibit...

urachal anomalies are exceptionally rare. they can present in different ways in childhood as well as in adults. we present an interesting case of vesico-urachal diverticulum with alternating sinus. the interesting finding in this patient was the inversion and disappearance of the umbilicus at the termination of voiding

The main result of the paper is a description of the maximal ideals in the modular group algebras of the finitary symmetric and alternating groups (provided the characteristic p of the ground field is greater than 2). For the symmetric group there are exactly p − 1 such ideals and for the alternating group there are (p − 1)/2 of them. The description is obtained in terms of the annihilators of ...

We present new algorithms for permutation group manipulation. Our methods result in an improvement of nearly an order of magnitude in the worst-case analysis for the fundamental problems of finding strong generating sets and testing membership. The normal structure of the group is brought into play even for such elementary issues. An essential element is the recognition of large alternating com...

Every tame, prime and alternating knot is equivalent to a tame, prime and alternating knot in regular position, with a common projection. In this work, we show that the Dehn presentation of the knot group of a tame, prime, alternating knot, with a regular and common projection has a finite and complete rewriting system. Although there are rules in the rewriting system with lefthand side a gener...