RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Forthcoming papers Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Mat. Zametki: Year: Volume: Issue: Page: Find

 Mat. Zametki, 1976, Volume 19, Issue 6, Pages 833–842 (Mi mz7804)

Semiplane lattices over irreducible groups

P. Ya. Grushko

Irkutsk State University

Abstract: Among transitive $G$-lattices we can distinguish a rather broad class of so-called semiplane lattices associated with the semidirect product of a Lie group $H$ and a certain automorphism group $G$ of it. It turns out that semiplane lattices are almost always plane in the irreducible case, i.e., we can take it that group $H$ is commutative. An exception is the case of the adjoined representation of a simple Lie group. We have also proved that if group $G$ is involutive and has a “small” radical, then all transitive $G$-lattices turn out to be semiplane.

Full text: PDF file (754 kB)

English version:
Mathematical Notes, 1976, 19:6, 491–496

Bibliographic databases:

UDC: 513

Citation: P. Ya. Grushko, “Semiplane lattices over irreducible groups”, Mat. Zametki, 19:6 (1976), 833–842; Math. Notes, 19:6 (1976), 491–496

Citation in format AMSBIB
\Bibitem{Gru76} \by P.~Ya.~Grushko \paper Semiplane lattices over irreducible groups \jour Mat. Zametki \yr 1976 \vol 19 \issue 6 \pages 833--842 \mathnet{http://mi.mathnet.ru/mz7804} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=498758} \zmath{https://zbmath.org/?q=an:0341.53021|0333.53029} \transl \jour Math. Notes \yr 1976 \vol 19 \issue 6 \pages 491--496 \crossref{https://doi.org/10.1007/BF01149924}