TY - JOUR
T1 - Every topological group is a group retract of a minimal group
AU - Megrelishvili, Michael
PY - 2008/10/15
Y1 - 2008/10/15
N2 - We show that every Hausdorff topological group is a group retract of a minimal topological group. This first was conjectured by Pestov in 1983. Our main result leads to a solution of some problems of Arhangel'skii. One of them is the problem about representability of a group as a quotient of a minimal group (Problem 519 in the first edition of 'Open Problems in Topology'). Our approach is based on generalized Heisenberg groups and on groups arising from group representations on Banach spaces.
AB - We show that every Hausdorff topological group is a group retract of a minimal topological group. This first was conjectured by Pestov in 1983. Our main result leads to a solution of some problems of Arhangel'skii. One of them is the problem about representability of a group as a quotient of a minimal group (Problem 519 in the first edition of 'Open Problems in Topology'). Our approach is based on generalized Heisenberg groups and on groups arising from group representations on Banach spaces.
KW - Group representation
KW - Heisenberg type group
KW - Matrix coefficient
KW - Minimal group
UR - https://www.scopus.com/pages/publications/52049122137
U2 - 10.1016/j.topol.2007.04.028
DO - 10.1016/j.topol.2007.04.028
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AN - SCOPUS:52049122137
SN - 0166-8641
VL - 155
SP - 2105
EP - 2127
JO - Topology and its Applications
JF - Topology and its Applications
IS - 17-18
ER -