Displaying similar documents to “Character sums in complex half-planes”

On the number of solutions of equation x p k = 1 in a finite group

Yakov Berkovich (1995)

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

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Theorem A yields the condition under which the number of solutions of equation x p k = 1 in a finite p -group is divisible by p n + k (here n is a fixed positive integer). Theorem B which is due to Avinoam Mann generalizes the counting part of the Sylow Theorem. We show in Theorems C and D that congruences for the number of cyclic subgroups of order p k which are true for abelian groups hold for more general finite groups (for example for groups with abelian Sylow p -subgroups).

Abelian quasinormal subgroups of groups

Stewart E. Stonehewer, Giovanni Zacher (2004)

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

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Let G be any group and let A be an abelian quasinormal subgroup of G . If n is any positive integer, either odd or divisible by 4 , then we prove that the subgroup A n is also quasinormal in G .

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 .