The Schur multiplier of a p-group with the derived subgroup of maximal order

Abstract

In this note, we give two bounds for the order of Schur multiplier of groups of order pⁿ and class c with derived subgroup of order $p^{n-2}$ $(p\ne 2).$ They improve the earlier upper bounds on the order of Schur multiplier of such groups, in particular the bounds of Moravec and Rai when $|G\prime |=p^{n-2}.$

Keywords:

• p-group
• Schur multiplier

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 20J99
• 20D15

Acknowledgments

The authors gratefully thank to the referee for the constructive comments and recommendations which definitely help to improve the readability of the paper. The third author was supported by the postdoctoral grant “CAPES-PRINT” at Federal University of Minas Gerais.