The ranks of central factor and commutator groups

作者：Kurdachenko Leonid A^*; Shumyatsky Pavel

来源：Mathematical Proceedings of the Cambridge Philosophical Society, 2013, 154(1): 63-69.

DOI：10.1017/S0305004112000412

The Schur Theorem says that if G is a group whose center Z(G) has finite index n, then the order of the derived group G%26apos; is finite and bounded by a number depending only on n. In this paper we show that if G is a finite group such that G/Z(G) has rank r, then the rank of G%26apos; is r-bounded. We also show that a similar result holds for a large class of infinite groups.

• 出版日期2013-1