Displaying similar documents to “The Hughes subgroup”

On absolutely-nilpotent of class k groups

Patrizia Longobardi, Trueman MacHenry, Mercede Maj, James Wiegold (1995)

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

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A group G in a variety V is said to be absolutely- V , and we write G ∈ A ⁢ V , if central extensions by G are again in V . Absolutely-abelian groups have been classified by F. R. Beyl. In this paper we concentrate upon the class A ⁢ N k of absolutely-nilpotent of class k groups. We prove some closure properties of the class A ⁢ N k and we show that every nilpotent of class k group can be embedded in an A ⁢ N k -gvoup. We describe all metacyclic A ⁢ N k -groups and we characterize 2 -generator and infinite 3 -generator A ⁢ N 2 -groups....

A note on a class of factorized p -groups

Enrico Jabara (2005)

Czechoslovak Mathematical Journal

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In this note we study finite p -groups G = A B admitting a factorization by an Abelian subgroup A and a subgroup B . As a consequence of our results we prove that if B contains an Abelian subgroup of index p n - 1 then G has derived length at most 2 n .

Infinite locally soluble k -Engel groups

Lucia Serena Spiezia (1992)

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

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In this paper we deal with the class E k * of groups G for which whenever we choose two infinite subsets X , Y there exist two elements x ∈ X , y ∈ Y such that x , y , … , y ︸ k = 1 . We prove that an infinite finitely generated soluble group in the class E k * is in the class E k of k -Engel groups. Furthermore, with k = 2 , we show that if G ∈ E 2 * is infinite locally soluble or hyperabelian group then G ∈ E 2 .

Injectors of fitting classes of 𝔊 1 -groups

Federico Menegazzo, Martin L. Newell (1988)

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

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Fitting classes and injectors are discussed in the class of 𝔊 1 -groups. A necessary and sufficient condition for the existence of injectors is given; it is also shown that, when this condition holds, the injectors form a unique conjugacy class.

A remark on a Theorem of J. G. Thompson

Bertram Huppert (1998)

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

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An important theorem by J. G. Thompson says that a finite group G is p -nilpotent if the prime p divides all degrees (larger than 1) of irreducible characters of G . Unlike many other cases, this theorem does not allow a similar statement for conjugacy classes. For we construct solvable groups of arbitrary p -lenght, in which the lenght of any conjugacy class of non central elements is divisible by p .