6533b857fe1ef96bd12b4d8c

RESEARCH PRODUCT

Extension of a Schur theorem to groups with a central factor with a bounded section rank

Javier OtalLeonid A. KurdachenkoAdolfo Ballester-bolinchesS. Camp-mora

subject

CombinatoricsMultiplier (Fourier analysis)Algebra and Number TheoryBounded functionSchur's lemmaCommutator subgroupFocal subgroup theoremRank of an abelian groupSchur's theoremSchur multiplierMathematics

description

Abstract A well-known result reported by Schur states that the derived subgroup of a group is finite provided its central factor is finite. Here we show that if the p-section rank of the central factor of a locally generalized radical group is bounded, then so is the p-section rank of its derived subgroup. We also give an explicit expression for this bound.

yearjournalcountryeditionlanguage
2013-11-01Journal of Algebra
https://doi.org/10.1016/j.jalgebra.2013.06.035