New PDF release: Aus dem Nachlass von R. Brauer

By Jørn Børling Olsson

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A. 6. and us that we can weaken this to lB rB \f(l,r) EE {(al,ar) : (l,r) ER, aEr}UW. E where n, together with the F-set structure of L;, tell Since B is an epimorphism, it must map the first part of E onto {(O"l,O"r) : (l,r) ER, O"EL;}. 4 Proposition The map;:Y will be an isomorphism if O"r rB and \fO"EL;, (l,r) ER \f(l,r)EW. S Corollary If the table is closed, and sl lB sr rB then SU will be an M-set isomorphic to \fsESU,(l,r)ER \f(l,r)EW n. This result tells us how to proceed. 4 and use the action with defining to evaluate the images under B of the two sides in L;.

London Math. Soc. 25 (1972), 603-614. [4] G. Baumslag and D. Solitar, Some TWo-Generator One-Relator Non-Hopfian Groups, Bull. Amer. Math. Soc. 68 (1962),199-201. [5] G. Baumslag, S. M. Gersten, M. Shapiro and H. Short, Automatic Groups and Amalgams, MSRI preprint. (A condensed version of this paper, without proofs, appears in G. Baumslag and C. F. ) [6] B. Benninghofen, S. Kemmerich and M. M. Richter, Systems of Reductions, Lecture Notes in Comput. Sci. 277, New York: Springer-Verlag, 1987. [7] M.

3 Processing relations We aim to modify the table, and so 'E, so that i becomes an isomorphism. 2, is equivalent to: \fi,TEr. A. 6. and us that we can weaken this to lB rB \f(l,r) EE {(al,ar) : (l,r) ER, aEr}UW. E where n, together with the F-set structure of L;, tell Since B is an epimorphism, it must map the first part of E onto {(O"l,O"r) : (l,r) ER, O"EL;}. 4 Proposition The map;:Y will be an isomorphism if O"r rB and \fO"EL;, (l,r) ER \f(l,r)EW. S Corollary If the table is closed, and sl lB sr rB then SU will be an M-set isomorphic to \fsESU,(l,r)ER \f(l,r)EW n.

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Aus dem Nachlass von R. Brauer by Jørn Børling Olsson


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