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Conjugacy classes, characters and products of elements
Author(s) -
Guralnick Robert M.,
Moretó Alexander
Publication year - 2019
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201800403
Subject(s) - mathematics , coprime integers , conjugacy class , pairwise comparison , nilpotent , order (exchange) , property (philosophy) , finite group , pure mathematics , simple (philosophy) , combinatorics , group (periodic table) , statistics , philosophy , chemistry , organic chemistry , finance , epistemology , economics
Recently, Baumslag and Wiegold proved that a finite group G is nilpotent if and only if o ( x y ) = o ( x ) o ( y ) for every x , y ∈ G of coprime order. Motivated by this result, we study the groups with the property that( x y ) G = x G y Gand those with the property that χ ( x y ) = χ ( x ) χ ( y ) for every χ ∈ Irr ( G ) and every nontrivial x , y ∈ G of pairwise coprime order. We also consider several ways of weakening the hypothesis on x and y . While the result of Baumslag and Wiegold is completely elementary, some of our arguments here depend on (parts of) the classification of finite simple groups.