Groups Generated by (near) Mutually Engel Periodic Pairs
Słanina, Piotr ; Tomaszewski, Witold
Bollettino dell'Unione Matematica Italiana, Tome 10-A (2007), p. 485-497 / Harvested from Biblioteca Digitale Italiana di Matematica
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We use notations: [x,y]=[x,1⁢y] and [x,k+1⁢y] e [[x,k⁢y],y]. We consider groups generated by x, y satisfying relations x=[x,n⁢y],y=[y,n⁢x] or [x,y]=[x,n⁢y], [y,x]=[y,n⁢x]. We call groups of the first type mep-groups and of the second type nmep-groups. We show many properties and examples of mep- and nmep-groups. We prove that if p is a prime then the group S⁢l2⁢(p) is a nmep-group. We give the necessary and sufficient conditions for metacyclic group to be a nmep-group and we show that nmep-groups with presentation ⟨x,y∣[x,y]=[x,2⁢y],[y,x]=[y,2⁢x],xn,ym⟩ are finite.

Scriviamo [x,y]=[x,1⁢y] e [x,k+1⁢y] e [[x,k⁢y],y]. Nel presente mostriamo certe proprietà ed esempio dei gruppi con i generatori x, y tali che x=[x,n⁢y],y=[y,n⁢x] o [x,y]=[x,n⁢y], [y,x]=[y,n⁢x].

Publié le : 2007-06-01
@article{BUMI_2007_8_10B_2_485_0,
     author = {Piotr S\l anina and Witold Tomaszewski},
     title = {Groups Generated by (near) Mutually Engel Periodic Pairs},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {10-A},
     year = {2007},
     pages = {485-497},
     zbl = {1167.20018},
     mrnumber = {2339456},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2007_8_10B_2_485_0}
}

Słanina, Piotr; Tomaszewski, Witold. Groups Generated by (near) Mutually Engel Periodic Pairs. Bollettino dell'Unione Matematica Italiana, Tome 10-A (2007) pp. 485-497. http://gdmltest.u-ga.fr/item/BUMI_2007_8_10B_2_485_0/

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