Homotopy Nilpotency in Localized Lie Groups

Daisuke Kishimoto, Kyoto University

It is known that p-localized Lie groups are homotopy commutative when
the prime p is large enough. However it is not known how far from being
homotopy commutative p-localized Lie groups are when p is not so large.
We consider this problem by using homotopy nilpotency and as a
consequence we see that homotopy nilpotency is not a monotonic
decreasing function in p.