ABSTRACT
The purpose of this paper is to classify the normal extensions G of a cyclic p-group , i.e.,
, with the irreducible character induced from a faithful linear character of
. In fact we determine all normal extensions G of a cyclic p-group
by p-subgroups of the automorphism group
with the centralizer
. Consequently, we have a theorem (Theorem 1) which might characterize the dihedral groups and the generalized quaternion groups of order
among non-abelian 2-groups.
ACKNOWLEDGMENT
The author would like to express his sincere gratitude to Professor Claus Michael Ringel, Professor Toshihiko Yamada and Professor Katsusuke Sekiguchi for their helpful suggestions.