3). 1 {¢ c I(M): ~ = ~ with nontrivial Let Fc I(M) be an L-subgroup, projection homomorphisms such that i) M1 is a Euclidean Pl(F) in I(M) of F.

Be a n L - s u b g r o u p , corresponding ÷ I(M2). a uniform o f N, i s 2) Let P~I(M) splitting ÷ I(~1) of the and l e t projection Let r 2 = p2(r) an L - s u b g r o u p M=MlXM2 be homomorphisms be a d i s c r e t e of I(M1). subgroup I f M1 i s lattice i n ~1 a n d C(F) n N= C ( N ) , abelian subgroup following of N with of a Euclidean the Clifford finite index i n N. occurs: rl=Pl(r) is discrete. If F *=N=kernel (p2) cI(M1) x{1} F2* = k e r n e l ( p l ) L { 1 ) x I(M2) , t h e n F i e h a s f i n i t e index a n d i n F 1.

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