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  • The commutator subgroup and Schur multiplier of a pair of finite p-groups

  • Part of
  • Ali Reza Salemkar, Mohammad Reza R. Moghaddam, Farshid Saeedi
  • Journal:
    Journal of the Australian Mathematical Society / Volume 81 / Issue 1 / August 2006
    Published online by Cambridge University Press:
    09 April 2009, pp. 1-10
    Print publication:
    August 2006
    • Article
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  • Let (M, G) be a pair of groups, in which M is a normal subgroup of G such that G/M and M/Z(M, G) are of orders pm and pn. respectively. In 1998, Ellis proved that the commutator subgroup [M, G] has order at most pn(n + 2 m−1)/2.

    In the present paper by assuming /[M, G] = pn(n+2m−1)/2, we determine the pair (M, G). An upper bound is obtained for the Schur multiplier of the pair (M, G), which generalizes the work of Green (1956).