(FUNDAMENTAL AND APPLIED MATHEMATICS)

2006, VOLUME 12, NUMBER 2, PAGES 17-38

## Almost completely decomposable groups with primary regulator quotients and their endomorphism rings

E. A. Blagoveshchenskaya

Abstract

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Let $X$ be a block-rigid almost completely decomposable group of ring type with regulator $A$ and $p$-primary regulator quotient $X/A$ such that $pl=expX/A$ with natural $l > 1$. From the well-known fact $plEnd A \subset End X \subset End A$ it follows that $End X = End X \cap End A$ and $plEnd A= End X \cap plEnd A$. Generalizing these, we determine the chain $End X = \mathcal E$A(l) ⊂ \mathcal EA(l−1) ⊂ \mathcal EA(l−2) ⊂ ... ⊂ \mathcal EA(1) ⊂ \mathcal EA(0) = End A, satisfying $pl-k\mathcal E$A(k) = End X ∩ pl−k End A, and construct groups $X\text{'}$k and $\widetilde\left\{X$k} such that $\mathcal E$A(k) = Hom (X'k, \widetilde{Xk}), where $k = 1,2,...,l$- 1.

Location: http://mech.math.msu.su/~fpm/eng/k06/k062/k06201h.htm