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Displaying similar documents to “Subgroups of -factorizable groups.”

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.

Subgroups of -factorizable groups

Constancio Hernández, Mihail G. Tkachenko (1998)

Commentationes Mathematicae Universitatis Carolinae

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

Homomorphic images of -factorizable groups

Mihail G. Tkachenko (2006)

Commentationes Mathematicae Universitatis Carolinae

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It is well known that every -factorizable group is ω -narrow, but not vice versa. One of the main problems regarding -factorizable groups is whether this class of groups is closed under taking continuous homomorphic images or, alternatively, whether every ω -narrow group is a continuous homomorphic image of an -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 -factorizable...