Then (RNQ(H), [symmetry]) is an [H.sub.v]-group with

identity element [bar.0] = (0, [p.summation over (i=1)] 0[T.sub.i], [r.summation over(j=1)] 0[I.sub.j], [s.summation over(k=1)] 0[F.sub.k]) if and only if (H, +) is an [H.sub.v]-group with an

identity element 0.

Theorem 49 Let (Eq.) be a symmetric semi open neighbourhood of the

identity element of a semi connected irresolute topological group

Now we describe a strategy of Derek for i < p such that at the endpoints of A1, A2, ..., [A.sub.i] the token will be at i different positions, also different from the

identity element, which is the starting position.

We call 1 as an

identity element of (m, n)-semiring (R, f, g).

Let e be the

identity element of the special loop ([L.sub.M], [omicron]).

Proof: The coefficient of the

identity element 1 in [A.sub.J] is 1.

A two-dimensional unital division algebra B is spanned by the

identity element 1 and some element b [member of] B \ R1.

All the three 3x3 Latin groups are cyclic, that is, there is an element x such that [x.sup.3] = e, the

identity element for each of these groups.

It has a compact support at {0} = ((0, 0); 0), the

identity element of G, so that u [member of] U.

Vollmer & Mills, 1966)--can form a tension for the profession because individual mental health counselors may weight

identity elements differently for the career path than the profession highlights in accomplishing its mission.

This shows that each and every non

identity element in G is a pendent vertex in Ne(G, I).