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By Gilbert Baumslag (auth.), Ann Chi Kim, Bernhard H. Neumann (eds.)

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Additional info for Groups — Korea 1983: Proceedings of a Conference on Combinatorial Group Theory, held at Kyoungju, Korea, August 26–31, 1983

Example text

Brown and J. Howie for many interesting discussions and useful remarks. 3. In particular, they thank K. Brown for his comments The first author acknowledges the financial assistance of a Glasgow University Postgraduate Award. Some of the new results contained in this paper will appear in the first author's doctoral dissertation. Notation Z , Z + , Z2 , @ , C will denote the integers, positive integers, or order 2, rationals (thought of as a group under addition), respectively. denoted by The highest common factor of two non-zero integers hcf(m, n) We write A ~f B , A ~ f B to indicate that B .

Principal present information filters by looking have some bearing Let LEMMA 3. (i) If about a principal We now show, dually, F ideal can be obtained by looking that we can obtain at atoms lying outside principal on Problem information ideals. about The results we 3. be a non-abelian free group. G = A ×B and @ :G + F is an epimorphism then contains one of Ker@ A, B . (ii) If Proof. trivial. A I ..... An ~ F (i) Suppose, Let then AI .... × An ~ F . by way of contradiction, Xl, x 2 E A¢\{l}, YI' Y2 c B¢\(I} .

Is subnormal in subsets of M I x ... x ~ n G then subnormal in L . G , K ~ L M ~ 2G if and o n l y if The quotient of the lattice of subG . Now, W i l s o n shows such that the normal closure of of the distinct conjugates o f K ~ Mil x ... , n} . on the lattice of subnormal structure lattice of ~2-subgroup is the direct product If and is called the has a subnormal of K , L K ~ Now it turns out that Mir G for some subset M in M in G . , ir} is isomorphic to the lattice of Id(G) is a chain of l e n g t h n : 44 M.

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