The intersection graph of a finite Moufang loop

Hamideh Hasanzadeh, Ali Iranmanesh

Abstract


The intersection graph ΓSI(G) of a group G with identity element e is the
graph whose vertex set is the set V (ΓSI(G)) = G-e and two distinct vertices x
and y are adjacent in ΓSI(G) if and only if |⟨x⟩∩⟨y⟩| > 1; where ⟨x⟩ is the cyclic
subgroup of G generated by x. In this paper, at first we obtain some results
for this graph for any Moufang loop. More specially we observe non-isomorphic
finite Moufang loops may have isomorphic intersection graphs.


Keywords


Loop theory, Intersection graph, Finite Moufang loop.

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