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Groups generated by two mutually Engel periodic elements

H. Heineken (2000)

Bollettino dell'Unione Matematica Italiana

Scriviamo [ x , y ] = [ x , 1 y ] ed [ [ x , k y ] , y ] = [ x , k + 1 y ] . Cerchiamo gruppi S L 2 , q con generatori x , y tali che [ x , m y ] = x ed [ y , n x ] = y per alcuni numeri naturali m , n .

Groups whose proper subgroups are locally finite-by-nilpotent

Amel Dilmi (2007)

Annales mathématiques Blaise Pascal

If 𝒳 is a class of groups, then a group G is said to be minimal non 𝒳 -group if all its proper subgroups are in the class 𝒳 , but G itself is not an 𝒳 -group. The main result of this note is that if c > 0 is an integer and if G is a minimal non ( ℒℱ ) 𝒩 (respectively, ( ℒℱ ) 𝒩 c )-group, then G is a finitely generated perfect group which has no non-trivial finite factor and such that G / F r a t ( G ) is an infinite simple group; where 𝒩 (respectively, 𝒩 c , ℒℱ ) denotes the class of nilpotent (respectively, nilpotent of class at most c , locally...

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