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

**Read Online or Download Groups — Korea 1983: Proceedings of a Conference on Combinatorial Group Theory, held at Kyoungju, Korea, August 26–31, 1983 PDF**

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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.