## Finitely Presented Infinite Simple GroupsDepartment of Pure Mathematics, Department of Mathematics, I.A.S., Australian National University, 1974 - Finite groups - 82 pages |

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abelian apply assume automorphism bases belongs characteristic characteristic element circuits columns complete condition congruence conjugacy classes consequence consisting construct contains correspondence d-fold expansion defining relations depth less determines diagram of depth elements of order embedding exists expressed extend finite finite order fixed Fn(X follows form with respect free algebra fundamental set G n,r given hence homomorphism induction infinite initial segment integers involves isomorphism Lemma mapping mean necessary nodes nontrivial normal Note Observe obtain operations orbit pair path permutation possible proof proper prove reduction relation of depth replace represented respect result rows satisfied semi-infinite orbit seminormal form Similarly simple solutions standard form subalgebra subgroup sufficient Suppose symbol THEOREM unique write αα αβ αβα αββ βα βαα ββ ββα