The following basic results on infinite locally finite subgroups of a free m-generŽ . 48 ator Burnside group B m, n of even exponent n, where m ) 1 and n G 2 , n is divisible by 29, are obtained: A clear complete description of all infinite groups that Ž . Ž . are embeddable in B m, n as maximal locally finite subgroups is given. Any Ž . infinite locally finite subgroup L of B m, n is contained...

How and/or on what were the URISC funds expended? URISC funds for this project were used as salary for my time, which included working 100 hours at $10 an hour. The URISC award allowed me to continue my research under the direction of Dr. McClelland.

We introduce ‘subgroup additivity’ as our main axiom and investigate its implications for the queueing problem. The axiom of subgroup additivity requires that a rule assigns the same expected ‘relative’ utility to each agent whether an agent’s expected relative utility is calculated from the problem involving all agents or from its sub-problems with a smaller number of agents. As a result, we p...

We discuss the following conjecture of Kitaoka: if a finite subgroup G of GLn(OK) is invariant under the action of Gal(K/Q) then it is contained in GLn(K ). Here OK is the ring of integers in a finite, Galois extension K of Q and K ab is the maximal, abelian subextension of K. Our main result reduces this conjecture to a special case of elementary abelian p−groups G. Also, we construct some new...

By the Shepherd–Leedham-Green–McKay theorem on finite p-groups of maximal class, if a finite p-group of order pn has nilpotency class n−1, then it has a subgroup of nilpotency class at most 2 with index bounded in terms of p. Counterexamples to a rank analogue of this theorem are constructed, which give a negative solution to Problem 16.103 in Kourovka Notebook. Moreover, it is shown that there...

The smallest known thick generalized octagon has order (2,4) and can be constructed from the parabolic subgroups of the Ree group 2F4(2). It is not known whether this generalized octagon is unique up to isomorphism. We show that it is unique up to isomorphism among those having a point a whose stabilizer in the automorphism group both fixes setwise every line on a and contains a subgroup that i...

We say that the width of an infinite subgroup H in G is n if there exists a collection of n essentially distinct conjugates of H such that the intersection of any two elements of the collection is infinite and n is maximal possible. We define the width of a finite subgroup to be 0. We prove that a quasiconvex subgroup of a negatively curved group has finite width. It follows that geometrically ...

This paper is an introduction to forcing axioms and large cardinals. Specifically, we shall discuss the large cardinal strength of forcing axioms in the presence of regularity properties for projective sets of reals. The new result shown in this paper says that ZFC + the bounded proper forcing axiom (BPFA) + “every projective set of reals is Lebesgue measurable” is equiconsistent with ZFC + “th...

Received 16 March 2008; accepted 4 May 2008 Abstract: We classify the maximal irreducible periodic subgroups of PGL(q,F) , where F is a field of positive characteristic p transcendental over its prime subfield, q 6= p is prime, and F× has an element of order q . That is, we construct a list of irreducible subgroups G of GL(q,F) containing the centre F×1q of GL(q,F) , such that G/F×1q is a maxim...