Tor decomposition of bup* (BZ/p)^n

Abstract

We decompose bup* (BZ/p)^n, the connective unitary $K-$theory with $p$-adic coefficients of the $n-$fold smash product of the classifying space for the cyclic group of prime order $p$, as a direct sum of some graded groups, which include the graded groups bup* (BZ/p) and $Tor^1_{\Z_p[v]}(bu_{p^*}(B\Z/p),bu_{p^*}(B\Z/p))[-1]$. We deal with the

results in \cite[Theorem $3.8$]{MK17} together with the K\"{u}nneth sequence for $bu_{p^*}(B\Z/p)^{\wedge n}$, to explain that there is no extension problem for this K\"{u}nneth sequence, for any finite number $n$ not just for $n=2$ and therefore the middle term of this sequence is a direct sum of the left
and the right side.