PUB - Publikationen an der Universität Bielefeld

In 2012, the second author obtained a description of the lattice of subgroups of a Chevalley group G(Phi, A) that contain the elementary subgroup E(Phi, K) over a subring K subset of A provided Phi = B-n, C-n, or F-4, n >= 2, and 2 is invertible in K. It turned out that this lattice is a disjoint union of "sandwiches" parametrized by the subrings R such that K subset of R subset of A. In the present paper, a similar result is proved in the case where Phi = C-n, n >= 3, and 2 = 0 in K. In this setting, more sandwiches are needed, namely those parametrized by the form rings (R, Lambda) such that K subset of Lambda subset of R subset of A. The result generalizes Ya. N. Nuzhin's theorem of 2013 concerning the root systems Phi = B-n, Cn, n >= 3, where the same description of the subgroup lattice is obtained, but under the condition that A and K are fields such that A is algebraic over K.