6533b853fe1ef96bd12accc5

RESEARCH PRODUCT

Incomplete vertices in the prime graph on conjugacy class sizes of finite groups

Emanuele PacificiSilvio DolfiLucia SanusCarlo Casolo

subject

CombinatoricsDiscrete mathematicsMathematics::Group TheoryVertex-transitive graphAlgebra and Number TheoryCirculant graphGraph powerSymmetric graphNeighbourhood (graph theory)Wheel graphDistance-regular graphComplement graphMathematics

description

Abstract Given a finite group G, consider the prime graph built on the set of conjugacy class sizes of G. Denoting by π 0 the set of vertices of this graph that are not adjacent to at least one other vertex, we show that the Hall π 0 -subgroups of G (which do exist) are metabelian.

yearjournalcountryeditionlanguage
2013-02-01Journal of Algebra
https://doi.org/10.1016/j.jalgebra.2012.10.012