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Permutability of centre-by-finite groups

Brunetto Piochi — 1989

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Let G be a group and m be an integer greater than or equal to 2 . G is said to be m -permutable if every product of m elements can be reordered at least in one way. We prove that, if G has a centre of finite index z , then G is ( 1 + [ z / 2 ] ) -permutable. More bounds are given on the least m such that G is m -permutable.

Su certi sistemi di leggi di varietà di gruppi risolubili

Brunetto Piochi — 1974

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

Let G be a supersolvable finite group or a solvable one, in which the orders of principal factors are primes or squares of primes; and let exp G divide n = p 1 a 1 p 2 a 2 p s a s ( p 1 > p 2 > > p s prime numbers). A much simple enunciation is given for essentially known theorems on some systems of laws characterizing G; it is indeed shown that the laws 1.(1) and 1.(2) can be removed from the enunciates of such theorems, getting equivalent systems of laws characterizing G.

Permutability of centre-by-finite groups

Brunetto Piochi — 1989

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

Let G be a group and m be an integer greater than or equal to 2 . G is said to be m -permutable if every product of m elements can be reordered at least in one way. We prove that, if G has a centre of finite index z , then G is ( 1 + [ z / 2 ] ) -permutable. More bounds are given on the least m such that G is m -permutable.

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