We introduce the concept of an infinite cochain sequence and initiate a theory of homological algebra for them. We show how these sequences simplify and improve the construction of infinite coclass families (as introduced by Eick and Leedham-Green) and how they apply in proving that almost all groups in such a family have equivalent Quillen categories. We also include some examples of infinite families of p-groups from different coclass families that have equivalent Quillen categories.
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