By C. M. Campbell, E. F. Robertson, T. C. Hurley, S. J. Tobin, J. Ward

This two-volume ebook comprises chosen papers from the foreign convention "Groups 1993 Galway/St Andrews", which used to be held at collage university Galway in August 1993. those volumes symbolize the wealth and variety of crew conception. 5 major lecture classes got on the convention. those have been "Geometry, Steinberg representations and complexity" by way of J. L. Alperin (Chicago), "Rickard equivalences and block idea" through M. Broué (ENS, Paris), "Cohomological finiteness stipulations" via P. H. Kropholler (QMW, London), "Counting finite index subgroups" by means of A. Lubotzky (Hebrew collage, Jerusalem), and "Lie equipment in staff thought" by way of E. I. Zel'manov (University of Wisconsin at Madison). Articles in accordance with their lectures, in a single case co-authored, shape a considerable a part of the lawsuits. one other major function of the convention used to be a spot workshop together run by means of J. NeubÜser and M. Schönert (RWTH, Aachen). articles through Professor NeubÜser, one co-authored, seem within the court cases. the opposite articles within the volumes include either refereed survey and examine articles contributed by way of different convention individuals. As with the complaints of the sooner "Groups-St Andrews" meetings, the articles in those lawsuits will, with their many references, end up necessary either to skilled researchers and to postgraduates drawn to team idea.

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MacDonald, Some p-groups of Frobenius and extra-special type, Israel [Mc2] [S] J. Math. 40(1981), 350-364. D. MacDonald, More on p-groups of Frobenius type, Israel J. Math. 56(1986), 335-394. G. Sorenson, Characters which vanish on all but three conjugacy classess, submitted. ON THE SATURATION OF FORMATIONS OF FINITE GROUPS A. M. EZQUERROt *Departament d'Algebra, Universitat de Valencia, C/ Dr. Moliner 50, 46100 Burjassot (Valencia), Spain tDepartamento de Matematica e Informatica, Universidad Publica de Navarra, Campus de Arrosadia, 31006 Pamplona, Spain 1.

Hence, b(,3) is a class of primitive groups of type 2. By Lemma 2, this implies that b(a) = 0. Then a = (E. Remark. Obviously in the soluble universe, such a simple group S with two different prime divisors does not exist. In this case, since F(p) = Sj for all primes p E chard \ 7r, we deduce that a = G r if chard = it and a = 67r 15 if it C char,'. So, Doerk's result is obtained. 3. The saturation of fj J. a With the notation of the preliminaries, denote X = 7) . There exists a trivial case of saturation of the class Sj 1 a.

Stl], Structure theorem for groups with infinitely many ends) Suppose that G is a finitely generated group with infinitely many ends. Then either G is a free product with amalgamation with a finite amalgamated subgroup or G is an HNN extension with one finite associated subgroup. Conversely, if G is either a free product with amalgamation with a finite amalgamated subgroup or G is an HNN extension with one finite associated subgroup then G has infinitely many ends except in the cases where G =G1 *K G2 with K finite, IG1 : KI = IG2 : KI = 2 or where G is an HNN extension with finite base K and associated subgroup K.