Beiträge zur Algebra und Geometrie / Contributions to Algebra and GeometryVol. 40, No. 1, pp. 243-260 (1999)

XC-Elements in Groups and Dietzmann Classes

Rudolf Maier, Jose Roberio Rogerio

Universidade de Brasilia, Departamento de Matematica - IE, BR - 70.910-900 Brasilia - DF, Brazil, e-mail:

Universidade Federal da Paraiba, Campus II, Departamento de Matematica e Estatistica, BR - 58.109-970 Campina Grande - PB, Brazil

Abstract: Group classes $D$ are investigated for which the following implication is generally true: $G/ C_G(x^G)\in\hbox{D}$ and $\langle x\rangle\in \hbox{\D} \Longrightarrow \langle x^G\rangle\in\hbox{D}.$

Classification (MSC91): 20F24, 20F25; 20F50

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