By Francis Borceux

Lecture notes in arithmetic No.1348

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Algebra 11 (1969), 195-212. Z. Hedrlin and A. Pultr, Symmetric relations (undirected graphs) with given semigroups, Monatsh. Math. 69 (1965), 318-322. [HP 66] , On full embeddings of categories of algebras, Illinois J. Math. 10 (1966), 392-406. [HP 65] H. Heineken and H. Liebeck, The occurrence of finite groups in the automorphism group of nilpotent groups of class 2, Arch. Math. 25 (1974), 8-16. [HL 74] [HCKN 71] P. Hell, V. Chvdtal, L. Kucera and J. Nesetril, Every finite graph is a full subgraph of a rigid graph, J.

19. Such sets do not exist in general for infinite groups, a fact that makes the proof for the infinite case substantially more difficult As a substitute for an irredundant generating set, one needs a large subset of a group which is free of the relation x-1y = y-1z. [Ba 78c]. Let us call a subset H of a group G good, if for any x,y,zeH, the relation x-1y = y-1z implies x=z. 3. Given a cardinal K, does there exist a group of power K without good subsets of the same cardinality? Let us call such groups strange.

19 (1979), 232-244. [BI 79] L. Babai and L. Lovdsz, Permutation groups and almost regular graphs, Studia Sci. Math. Hung. 8 (1973), 141-150. [BL 73] [BP 78] L. Babai and F. Pastijn, On semigroups with high symmetry, Simon Stevin 52 (1978), 73-84. L. Babai and A. Pultr, Endomorphism monoids and topological subgraphs of graphs, J. Comb. Theory - B 28 (1980) 278-283. L. Biggs, Algebraic Graph Theory, Cambridge Univ. Press, [Bi 74] Cambridge 1974. L. White, Permutation groups and Combinatorial Structures, London Math.