Diagonal resolutions for metacyclic groups

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• 作者：F.E.A. Johnson ; ^{feaj@math.ucl.ac.uk} ; J.J. Remez ^{j.remez@alumni.ucl.ac.uk}
• 关键词：primary ; 16E05 ; 20C10 ; secondary ; 18E30
• 刊名：Journal of Algebra
• 出版年：2017
• 出版时间：15 March 2017
• 年：2017
• 卷：474
• 期：Complete
• 页码：329-360
• 全文大小：557 K
• 卷排序：474

文摘

We show the finite metacyclic groups G(p,q)G(p,q) admit a class of projective resolutions which are periodic of period 2q   and which in addition possess the properties that a) the differentials are 2×22×2diagonal matrices; b) the Swan–Wall finiteness obstruction (cf.  and ) vanishes. We obtain thereby a purely algebraic proof of Petrie's Theorem ([14]) that G(p,q)G(p,q) has free period 2q.