Commuting Involution Graphs for Ãn
نویسنده
چکیده
Let G be a group and X a subset of G. The commuting graph on X, denoted C(G,X), has vertex set X and an edge joining x, y ∈ X whenever xy = yx. If in addition X is a set of involutions, then C(G,X) is called a commuting involution graph. Commuting graphs have been investigated by many authors. Sometimes they are tools used in the proof of a theorem, or they may be studied as a way of shedding light on the structures of certain groups (as in [1]). Commuting involution graphs for the case where X is a conjugacy class of involutions were studied by Fischer [4] – in that case X was the class of 3-transpositions of a 3-transposition group. These groups include all finite simply laced Weyl groups, in particular the symmetric group.
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Commuting Involution Graphs for 3-Dimensional Unitary Groups
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