Errata: SUBGROUPS of the ISOMETRY GROUP of the PLANE [1]

James M. Parks

SUNY Potsdam

The following lemma replaces the lemma in [1], p. 407. While the lemma in [1] is true it does not cover all situations which occur in the examples which follow.

This will clarify the arguments in Examples 1, 2, 4, and 5, where it is required that the subgroup Trans be normal in some subgroup S of Iso.

The proof follows by the same reasoning as used for the lemma being replaced (see [1]).

Lemma. If a subgroup S of Iso(3) contains the subgroup Trans(3), Trans(3) < S < Iso(3), then Trans(3) is normal in S, Trans(3)< S.

It must also be said that the results in [1] are not implied to be comprehensive, but rather indicative of the type which are available in this area.

1. J. Parks, SUBGROUPS of the ISOMETRY GROUP of the PLANE, J. Geom. & Topo., 7(3),(07), 405-422.