 
Summary: JOUBNAL OF ALGEBRA 6, 222241 (1967)
Sylow Intersections and Fusion
J. L. ALPERIN*
Department of Mathematics, University of Chicago, Illinois 60637
Communicated by I. N. Herstein
Received July 12, 1966
1. INTRODUCTION
It is common in mathematics for a subject to have its local and global
aspects; such is the case in group theory. For example, the structure and
embedding of subgroups of a group G may be usefully thought of as part of
the local structure of G while the normal subgroups, quotient groups and
conjugacy classes are relevant to the global structure of G. Furthermore, the
connections between local and global structure are very important. In the
study of these relations, the methods of representation theory and transfer
are very useful. The application of these techniques is often based upon
results concerning the fusion of elements. (Recall that two elements of a
subgroup H of a group G are said to be ficsed if they are conjugate in G but
not in H.) Indeed, the formula for induced characters clearly illustrates this
dependence. However, more pertinent to the present work, and also indica
tive of this connection with fusion, is the focal subgroup theorem [8]: if P
