J. Aust. Math. Soc.
81 (2006), 19

The commutator subgroup and Schur multiplier of a pair of finite
pgroups


Mohammad Reza R. Moghaddam
Centre of Excelence in
Analysis on Algebraic Structures
(President)
and
Faculty of Mathematical Sciences
Ferdowsi University of Mashhad
Iran
moghadam@math.um.ac.ir





Abstract

Let be a pair of groups, in which
is a normal subgroup of
such that
and
are of orders
and
, respectively. In 1998, Ellis proved that the
commutator subgroup
has order at most
.
In the present paper by assuming
, we determine the pair
. An upper bound is obtained for the Schur
multiplier of the pair
, which generalizes the work of Green (1956).

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