2,569 research outputs found
On the Order of Nilpotent Multipliers of Finite p-Groups
Let be a finite -group of order . YA. G. Berkovich (Journal of
Algebra {\bf 144}, 269-272 (1991)) proved that is elementary abelian
-group if and only if the order of its Schur multiplier, , is at the
maximum case. In this paper, first we find the upper bound
for the order the -nilpotent multiplier of ,
, where is the number of basic commutators of
weight on letters. Second, we obtain the structure of , in abelian
case, where , for all .
Finally, by putting a condition on the kernel of the left natural map of the
generalized Stallings-Stammbach five term exact sequence, we show that an
arbitrary finite -group with the -nilpotent multiplier of maximum order
is an elementary abelian -group.Comment: 14 page
On the Order of the Schur Multiplier of a Pair of Finite p-Groups
In 1998, G. Ellis defined the Schur multiplier of a pair of groups
and mentioned that this notion is a useful tool for studying pairs of groups.
In this paper, we characterize the structure of a pair of finite -groups
in terms of the order of the Schur multiplier of under some
conditions.Comment: 11 pages, to appear in Journal of Advanced Research in Pure
Mathematic
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