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The Moufang condition
Some features of special pgroups
Parameters of elation quadrangles and structure of elation groups
abelian group acts sharply transitively acts transitively automorphism group BN-pair center of transitivity chain complex chapter cohomology collinear commutator Coxeter Coxeter group deﬁne deﬁnition denote elation generalized quadrangle elation group elation point elation quadrangles Exercise ﬁeld ﬁnite ﬁrst ﬁx ﬁxed pointwise ﬁxes ﬁxing ﬂag ﬂock GQ ﬂock quadrangle Frobenius group Frobenius kernel G Fq geometry GQ of order group G group of whorls Heisenberg group i-root containing inﬁnite involution isomorphic Kantor family Kantor—Knuth Lemma Let G Lie algebra line incident linewise Moufang conditions Moufang quadrangle nilpotent normal subgroup Note order q2 ovoid p-group pg(n point 00 points not collinear prime power projective space Proof q-clan regular point result root-elations satisﬁed set of elations Show standard elations subGQ of order subgroup of G subspaces Suppose Sylow p-subgroup Theorem Theorem 1.3 thick ﬁnite thick GQ thick subGQ translation group translation point