Tarski Monster Group
In
mathematics
, a
Tarski monster group
, named for
Alfred Tarski
, is an infinite
group
G
, such that every proper subgroup
H
of
G
, other than the identity subgroup, is a
cyclic group
of order a fixed
prime number
p
. Such groups are now known to exist. This was shown by Ol'shanskii in 1979. They are a source of
counterexamples
in other questions in
group theory
.
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