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A bound on the Schur multiplier of a prime-power group

  • Graham Ellis (a1) and James Wiegold (a2)

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The paper improves on an upper bound for the order of the Schur multiplier of a finite p-group given by Wiegold in 1969. The new bound is applied to the problem of classifying p-groups according to the size of their Schur multipliers.

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References

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[1]Berkovich, Ya.G., ‘On the order of the commutator subgroup and Schur multiplier of a finite p-group’, J. Algebra 144 (1991), 269272.
[2]Beyl, F.R. and Tappe, J., Group extensions, representations, and the Schur multiplicator, Lecture Notes in Math. 958 (Springer-Verlag, Berlin, Heidelberg, New York, 1982).
[3]Ellis, G., ‘A bound for the derived and Frattini subgroups of a prime-power group’, Proc. Amer. Math. Soc. 126 (1998), 25132523.
[4]Ellis, G., ‘On the Schur multiplier of p-groups’, Comm. Algebra (to appear).
[5]Gaschütz, W., Neubüser, J. and Yen, Ti, ‘Über den Multiplikator von p-Gruppen’, Math. Z. 100 (1967), 9396.
[6]Wiegold, J., ‘Commutator subgroups of finite p-groups’, J. Austral. Math. Soc. 10 (1969), 480484.
[7]Zhou, X., ‘On the order of Schur multipliers of finite p-groups’, Comm. Algebra 22 (1994), 18.
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A bound on the Schur multiplier of a prime-power group

  • Graham Ellis (a1) and James Wiegold (a2)

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