Commutativity preserving extensions of groups
2017 ◽
Vol 148
(3)
◽
pp. 575-592
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In parallel to the classical theory of central extensions of groups, we develop a version for extensions that preserve commutativity. It is shown that the Bogomolov multiplier is a universal object parametrizing such extensions of a given group. Maximal and minimal extensions are inspected, and a connection with commuting probability is explored. Such considerations produce bounds for the exponent and rank of the Bogomolov multiplier.
Keyword(s):
1986 ◽
Keyword(s):
2016 ◽
Vol 33
(6)
◽
pp. 1141
◽
1981 ◽
Vol 32
(3)
◽
pp. 286-295
◽
1971 ◽
Vol 62
(4)
◽
pp. 493-500
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Keyword(s):
1986 ◽
Vol 100
(2)
◽
pp. 281-301
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