On 2-swelling topological groups

Abstract: A topological group

G

is called 2-swelling if for any compact subsets

A, B s u b s e t G

and elements

a, b, c i n G

the inclusions

a A c u p b B s u b s e t A c u p B

and

a A c a p b B s u b s e t c (A c a p B)

are equivalent to the equalities

a A c u p b B = A c u p B

and

a A c a p b B = c (A c a p B)

. We prove that an (abelian) topological group

G

is 2-swelling if each 3-generated (resp. 2-generated) subgroup of

G

is discrete. This implies that the additive group

m a t h b b Q

of rationals is 2-swelling and each locally finite topological group is 2-swelling.

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