Automorphism groups of finite distributive lattices with a given sublattice of fixed points |
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| Authors: | M E Adams L Babai J Sichler |
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| Institution: | (1) State University of New York, 12562 New Paltz, NY, USA;(2) University of Manitoba, R3T 2N2 Winnipeg, Manitoba, Canada;(3) Eötvös Loránd University, Budapest, Hungary;(4) Université de Montréal, H3C 3J7 Montréal, Québec, Canada |
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| Abstract: | For a latticeL, a L is a fixed point ofL if and only iff(a)=a for every automorphismf ofL. Let Aut (L) andS (L) denote the group of automorphisms ofL and the sublattice of fixed points ofL, respectively. It is shown that ifG is a finite group other thanZ
2
2
,Z
2
3
,Z
2
4
,Z
3
2
or the quaternion group of order 8 andL is a finite automorphism free distributive lattice that is not near Boolean then there is a finite distributive latticeL such that Aut (L) G andS(L)L.The support of the National Research Council of Canada is gratefully acknowledged. |
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