### On Hall subgroups of a finite group

Wenbin Guo, Alexander Skiba (2013)

Open Mathematics

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New criteria of existence and conjugacy of Hall subgroups of finite groups are given.

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Wenbin Guo, Alexander Skiba (2013)

Open Mathematics

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New criteria of existence and conjugacy of Hall subgroups of finite groups are given.

Constancio Hernández, Mihail G. Tkachenko (1998)

Commentationes Mathematicae Universitatis Carolinae

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The properties of $\mathbb{R}$-factorizable groups and their subgroups are studied. We show that a locally compact group $G$ is $\mathbb{R}$-factorizable if and only if $G$ is $\sigma $-compact. It is proved that a subgroup $H$ of an $\mathbb{R}$-factorizable group $G$ is $\mathbb{R}$-factorizable if and only if $H$ is $z$-embedded in $G$. Therefore, a subgroup of an $\mathbb{R}$-factorizable group need not be $\mathbb{R}$-factorizable, and we present a method for constructing non-$\mathbb{R}$-factorizable dense subgroups of a special class of $\mathbb{R}$-factorizable groups. Finally, we construct...

Arad, Zvi, Herfort, Wolfgang (2005)

Journal of Lie Theory

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Mihail G. Tkachenko (2006)

Commentationes Mathematicae Universitatis Carolinae

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It is well known that every $\mathbb{R}$-factorizable group is $\omega $-narrow, but not vice versa. One of the main problems regarding $\mathbb{R}$-factorizable groups is whether this class of groups is closed under taking continuous homomorphic images or, alternatively, whether every $\omega $-narrow group is a continuous homomorphic image of an $\mathbb{R}$-factorizable group. Here we show that the second hypothesis is definitely false. This result follows from the theorem stating that if a continuous homomorphic image of an $\mathbb{R}$-factorizable...

Gong, Ming-Peng (1996)

Portugaliae Mathematica

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Mihail G. Tkachenko (1988)

Czechoslovak Mathematical Journal

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Ocampo Uribe, Oscar Eduardo (2010)

Revista Colombiana de Matemáticas

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