TY - UNPB
T1 - Permutation groups and normal subgroups
AU - Praeger, Cheryl E.
PY - 2003/4/15
Y1 - 2003/4/15
N2 - Various descending chains of subgroups of a finite permutation group can be used to define a sequence of `basic' permutation groups that are analogues of composition factors for abstract finite groups. Primitive groups have been the traditional choice for this purpose, but some combinatorial applications require different kinds of basic groups, such as quasiprimitive groups, that are defined by properties of their normal subgroups. Quasiprimitive groups admit similar analyses to primitive groups, share many of their properties, and have been used successfully, for example to study $s$-arc transitive graphs. Moreover investigating them has led to new results about finite simple groups.
AB - Various descending chains of subgroups of a finite permutation group can be used to define a sequence of `basic' permutation groups that are analogues of composition factors for abstract finite groups. Primitive groups have been the traditional choice for this purpose, but some combinatorial applications require different kinds of basic groups, such as quasiprimitive groups, that are defined by properties of their normal subgroups. Quasiprimitive groups admit similar analyses to primitive groups, share many of their properties, and have been used successfully, for example to study $s$-arc transitive graphs. Moreover investigating them has led to new results about finite simple groups.
KW - math.GR
KW - 20B05, 20B10 20B25, 05C25
M3 - Preprint
T3 - Proceedings of the ICM, Beijing
BT - Permutation groups and normal subgroups
ER -