p-groups are not determined by their integral cohomology groups

Ian J. Leary
Faculty of Math. Studies, Univ. of Southampton, SO17 1BJ,  UK.  

For each prime p, we exhibit pairs of p-groups all of whose integral
cohomology groups are isomorphic. The method used involves very little
calculation. The groups are exhibited as kernels of homomorphisms from
a compact Lie group G to U(1), and the main result is that kernels of
`similar' elements of Hom(G,U(1)) have isomorphic integral cohomology
groups.  

Bull. London Math. Soc. 27 (1995), 585-589. 


Unfortunately, the pair of 2-groups given in the original paper had
isomorphic integral cohomology for the trivial reason that the groups
were themselves isomorphic to each other! (I am indebted to Martin
Wursthorn who spotted this.) This was easily repaired, but
necessitated an erratum. The mistake arose because I miscalculated the
multiplicative order of a 2-by-2 matrix.  

Bull. London Math. Soc. 29 (1997) 368. 

In the dvi file in the archive the above error has been corrected.