On egglike inversive planes

Set of involutions arising from an egglike inversive plane

“…Let and F be a set and a family of involutions of as in [8]. Denoted by P the set ∪ F, we have |P | = n 3 + n 2 + n + 1 and the pair ( , C) is an inversive plane (see [8]).…”

“…Denoted by P the set ∪ F, we have |P | = n 3 + n 2 + n + 1 and the pair ( , C) is an inversive plane (see [8]). In the sequel two involutions f and g are said to be orthogonal if their circles are orthogonal.…”

“…. , n − 2) commutes with h and, by (3.1) in [8], it is orthogonal to h and since f 0 is orthogonal to h, by O 2 we have C f 0 ∩ C g i = {x}, i.e. g i ∈ x ∨ f 0 (i = 1, .…”

“…Korchmaros and Olanda [8] investigated the properties of a family F(K) of involutions of a set which ensure that (K, F(K)) be an inversive plane. More precisely, they consider a set of n 2 +1 points and a family F of involutions of , satisfying the following properties.…”

“…For any involution f ∈ F, the subset C f of fixed points of f has cardinality n + 1 (see [8]) and is called the circle associated with f . Denoted by C the set of these circles, using a result of Dembowski and Hughes (see Theorem 1.2) Korchmaros and Olanda proved the following Theorem.…”