An element g in a group G is called reversible (or real) if it is conjugate to g(-1) in G, i.e., there exists h in G such that g(-1) = hgh-1. The element g is called strongly reversible if the conjugating element h is an involution (i.e., element of order at most two) in G. In this paper, we classify reversible and strongly reversible elements in the isometry groups of F-Hermitian spaces, where F = C or H. More precisely, we classify reversible and strongly reversible elements in the groups Sp(n) alpha H-n, U(n) alpha C-n and SU(n) alpha C-n. We also give a new proof of the classification of strongly reversible elements in Sp(n). (c) 2022 Elsevier Inc. All rights reserved.
Reversible elementsReal elementsStrongly reversible elementsStrongly real elementsHermitian spaceUnitary groupsAffine isometriesPRODUCTS
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