Abstract
The replacement property (or Steinitz Exchange Lemma) for vector spaces has a natural analog for finite groups and their generating sets. For the special case of the groups where p is a prime larger than 5, first partial results concerning the replacement property were published by Benjamin Nachman (Citation2014). Second partial results were published by Hy P.G. Lam (Citation2017). The main goal of this paper is to provide a complete answer for
Acknowledgement
The authors are thankful to R. K. Dennis for patiently and carefully teaching us the requisite information needed for this paper and for guiding our inquiries in fruitful directions. Further thanks goes to the math department at Cornell University for hosting the SPUR/REU program and of course to our group mates without whom progress would have been far slower and less enjoyable. Finally, we would like to thank the referee for providing useful comments on how to improve the paper.