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Fundam. Prikl. Mat., 2006, Volume 12, Issue 2, Pages 17–38 (Mi fpm932)  

This article is cited in 1 scientific paper (total in 1 paper)

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

E. A. Blagoveshchenskaya

Saint-Petersburg State Polytechnical University

Abstract: 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 $p^l=\exp X/A$ with natural $l>1$. From the well-known fact $p^l\operatorname{End}A\subset\operatorname{End}X\subset\operatorname{End}A$ it follows that $\operatorname{End}X=\operatorname{End}X\cap\operatorname{End}A$ and $p^l\operatorname{End}A=\operatorname{End}X\cap p^l\operatorname{End}A$. Generalizing these, we determine the chain $\operatorname{End}X=\mathcal E_A^{(l)}\subset\mathcal E_A^{(l-1)}\subset\mathcal E_A^{(l-2)}\subset…\subset\mathcal E_A^{(1)}\subset\mathcal E_A^{(0)}=\operatorname{End}A$, satisfying $p^{l-k}\mathcal E_A^{({k})}=\operatorname{End}X\cap p^{l-k}\operatorname{End}A$, and construct groups $X'_k$ and $\widetilde{X_k}$ such that $\mathcal E_A^{({k})}=\operatorname{Hom}(X'_k,\widetilde{X_k})$, where $k=1,2,…,l-1$.

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English version:
Journal of Mathematical Sciences (New York), 2008, 149:2, 1047–1062

Bibliographic databases:

UDC: 512.541+512.553.5

Citation: E. A. Blagoveshchenskaya, “Almost completely decomposable groups with primary regulator quotients and their endomorphism rings”, Fundam. Prikl. Mat., 12:2 (2006), 17–38; J. Math. Sci., 149:2 (2008), 1047–1062

Citation in format AMSBIB
\Bibitem{Bla06}
\by E.~A.~Blagoveshchenskaya
\paper Almost completely decomposable groups with primary regulator quotients and their endomorphism rings
\jour Fundam. Prikl. Mat.
\yr 2006
\vol 12
\issue 2
\pages 17--38
\mathnet{http://mi.mathnet.ru/fpm932}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2249690}
\zmath{https://zbmath.org/?q=an:1160.20051}
\transl
\jour J. Math. Sci.
\yr 2008
\vol 149
\issue 2
\pages 1047--1062
\crossref{https://doi.org/10.1007/s10958-008-0044-x}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-38549092058}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. E. A. Blagoveshchenskaya, “Cyclic regulator quotient groups in the class of almost completely decomposable groups”, J. Math. Sci., 206:6 (2015), 623–628  mathnet  crossref  mathscinet
  • Фундаментальная и прикладная математика
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