THEOREM. Let G be a finite group and s an involution in G, such that CG(S)~CGQ(SO)Assume G^Co(s)0(G) (0(G) is the maximal normal odd order subgroup of G). Then Gc^Go. In particular, G has the following properties : (i) G has order 2 • 3 • 5 • 7 • 11 • 23, and is simple. (ii) G has two conjugacy classes of involutions. One class is represented by the involution s. A representative t of the secon...

We give a classification of irreducible characters of finite groups of Lie type of p′-degree, where p is any prime different from the defining characteristic, in terms of local data. More precisely, we give a classification in terms of data related to the normalizer of a suitable Levi subgroup, which in many cases coincides with the normalizer of a Sylow p-subgroup. The McKay conjecture asserts...

Methods for determining a generating set for the normalizer of a finite group of n X n integral matrices, i.e., an «-dimensional crystallographic point group, are discussed. Necessary and sufficient conditions for the finiteness of such a normalizer are derived, and several examples of the application of the methods to cases when the normalizer is infinite are presented. This is the third in a ...

For a group G, let U be the group of units of the integral group ring ZG. The group G is said to have the normalizer property if NU (G) = Z(U)G. It is shown that Blackburn groups have the normalizer property. These are the groups which have non-normal finite subgroups, with the intersection of all of them being nontrivial. Groups G for which class-preserving automorphisms are inner automorphism...

A 2-Sylow subgroup of J is elementary abelian of order 8 and J has no subgroup of index 2. If r is an involution in J, then C(r) = (r) X K, where K _ A5. Let G be a finite group with the following properties: (a) S2-subgroups of G are abelian; (b) G has no subgroup of index 2; and (c) G contains an involution t such that 0(t) = (t) X F, where F A5. Then G is a (new) simple group isomorphic to J...

The utility of data-driven techniques in the end-to-end problem of temporal information extraction is unclear. Recognition of temporal expressions yields readily to machine learning, but normalization seems to call for a rule-based approach. We explore two aspects of the (potential) utility of data-driven methods in the temporal information extraction task. First, we look at whether improving r...

Given a set r of permutations of an n-set, let G be the group of permutations generated by r. I f p is any prime, it is known that a Sylow p-subgroup P of G can be found in polynomial time. We show that the normalizer of P can also be found in polynomial time. In particular, given two Sylow p-subgroups of G, all elements conjugating one to the other can be found (as a coset of the normalizer of...

In this paper we present an Agda formalization of a normalizer for simply-typed lambda terms. The first step is to write a coinductive evaluator using the delay monad. The other component of the normalizer, a type-directed reifier from values to η-long β -normal forms, resides in the delay monad as well. Their composition, normalization-by-evaluation, is shown to be a total function, using a st...