We characterize the automorphism groups of circulant digraphs whose connection sets are relatively small, and of unit circulant digraphs. For each class, we either explicitly determine the automorphism group or we show that the graph is a “normal” circulant, so the automorphism group is contained in the normalizer of a cycle. Then we use these characterizations to prove results on the automorph...

We prove that the normalizer of any diffuse amenable subalgebra of a free group factor L(Fr) generates an amenable von Neumann subalgebra. Moreover, any II1 factor of the form Q ⊗̄L(Fr), with Q an arbitrary subfactor of a tensor product of free group factors, has no Cartan subalgebras. We also prove that if a free ergodic measure preserving action of a free group Fr, 2 ≤ r ≤ ∞, on a probability ...

We show how testing convertibility of two types in dependently typed systems can advantageously be implemented instead untyped normalization by evaluation, thereby reusing existing compilers and runtime environments for stock functional languages, without peeking under the hood, for a fast yet cheap system in terms of implementation effort. Our focus is on performance of untyped normalization b...

An extensive study and analysis of the concepts, classification, presentation, and nomenclature of chirality and lack of chirality in crystal structures and their constituents is presented. Oriented crystal structures are classified. The chirality rules for existence of molecular crystal structures are examined and the relation to segmentation and latent symmetry highlighted. The nomenclature o...

We prove that there exists an integer p0 such that X split (p)(Q) is made of cusps and CM-points for any prime p > p0. Equivalently, for any non-CM elliptic curve E over Q and any prime p > p0 the image of Gal(¯ Q/Q) by the representation induced by the Galois action on the p-division points of E is not contained in the normalizer of a split Cartan subgroup. This gives a partial answer to an ol...

We analyze a normalization function for the simply typed λ-calculus based on hereditary substitutions, a technique developed by Pfenning et al. The normalizer is implemented in Agda, a total language where all programs terminate. It requires no termination proof since it is structurally recursive which is recognized by Agda’s termination checker. Using Agda as an interactive theorem prover we e...

It is knwon [23] that if p is odd, NpT is isomorphic to the semidirect product T oWp, and the fibration (BT )p (BNpT )p BWp has a section. The classifying spaces of NpT and other p–toral subgroups of K have been extensively used for the study of BK at the prime p, [13] etc. We note, however, that for the normalizer NT the loop space of (BNT )p need not be a p–compact toral group. In fact, if p ...

1. In [3], we have shown that in a finite ZP-group G in which A and B are cyclic and A is its own normalizer, the commutator subgroup T of G is cyclic and G = AT with AC\T= I. This result can be used to determine the structure of arbitrary ZP-groups in which A and B are cyclic. If A is a subgroup of a group G, define the subgroup Ni(A) of G inductively by the formula Ni(A)=No(Ni~1(A)), and deno...