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- W1808770710 abstract "<p>A Hausdorff topological group G=(G,T) has the small subgroup generating property<br />(briefly: has the SSGP property, or is an SSGP group) if for each neighborhood U of $1_G$ there is a family $sH$<br />of subgroups of $G$ such that $bigcupsHsubseteq U$ and<br />$langlebigcupsHrangle$ is dense in $G$. The class of $rm{SSGP}$ groups is defined and investigated with respect<br />to the properties usually studied by topologists (products,<br />quotients, passage to dense subgroups, and the like), and with respect to the familiar class of minimally almost<br />periodic groups (the m.a.p. groups). Additional classes<br />SSGP(n) for $n<omega$ (with SSGP(1) = SSGP) are defined and investigated, and the class-theoretic inclusions<br />$$mathrm{SSGP}(n)subseteqmathrm{SSGP}(n+1)subseteqmathrm{ m.a.p.}$$<br />are established and shown proper.</p><p>In passing the authors also establish the presence of {rm SSGP}$(1)$ or {rm SSGP}$(2)$ in many of the early examples in the literature of abelian m.a.p. groups.</p>" @default.
- W1808770710 created "2016-06-24" @default.
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- W1808770710 date "2015-10-01" @default.
- W1808770710 modified "2023-10-14" @default.
- W1808770710 title "Some classes of minimally almost periodic topological groups" @default.
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- W1808770710 doi "https://doi.org/10.4995/agt.2015.3312" @default.
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