On zero-sum free subsets of length 7.

Yuan, Pingzhi; Zeng, Xiangneng

Displaying similar documents to “On zero-sum free subsets of length 7.”

On subsequence sums of a zero-sum free sequence. II.

Gao, Weidong, Li, Yuanlin, Peng, Jiangtao, Sun, Fang (2008)

The Electronic Journal of Combinatorics [electronic only]

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On subsequence sums of a zero-sum free sequence.

Sun, Fang (2007)

The Electronic Journal of Combinatorics [electronic only]

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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).