Then semi interior of any invariant subgroup of (Eq.) is an irresolute topological invariant subgroup again.
Then semi closure of any invariant subgroup of is an irresolute topological invariant subgroup again.
For cases 2-5, 9, 10, we use a particular fully invariant subgroup corresponding to the fundamental group of a torus or a Klein bottle that allows us to compute N(f) using fiberwise techniques.
For arbitrary selfmaps, it is more manageable to classify these maps up to fiberwise homotopy since for all but two of the ten cases, the flat manifold M fibers over [S.sup.1] with typical fiber N corresponding to a fully invariant subgroup of [[pi].sub.1](M).
He reviews basic definitions of groups and operations with whole numbers, groups of permutation, the concept of isomorphism, cyclical subgroups of a given group, simple groups of movement, invariant subgroups
, homomorphic mappings, and partitioning a group relative to a given subgroup.