Abstract
Let L, M, N be positive definite quadratic lattices over Z. We treated the following problem in [5], [6]:If L ⊗ M is isometric to L ⊗ N, then is M isometric to N?We gave a condition (**) in [6] such that the answer is affirmative for an indecomposable lattice L satisfying (**), and we gave some examples. In this paper we introduce a certain apparently weaker condition (A) than the condition (**), and we show that the condition (A) implies the condition (**) and more on integral orthogonal groups than a result in [6].
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