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434:, An infinite group with subgroups of prime orders, Math. USSR Izv. 16 (1981), 279–289; translation of Izvestia Akad. Nauk SSSR Ser. Matem. 44 (1980), 309–321.
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440:, Groups of bounded period with subgroups of prime order, Algebra and Logic 21 (1983), 369–418; translation of Algebra i Logika 21 (1982), 553–618.
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This article is about the kind of infinite group known as a Tarski monster group. For the largest of the sporadic finite simple groups, see
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is necessarily finitely generated. In fact it is generated by every two non-commuting elements.
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if every nontrivial subgroup (i.e. every subgroup other than 1 and G itself) has
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in 1979 that Tarski groups exist, and that there is a Tarski
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The construction of
Olshanskii shows in fact that there are
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non-isomorphic Tarski
Monster groups for each prime
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75:. A Tarski monster group is necessarily
37:In the area of modern algebra known as
27:Type of infinite group in group theory
158:is called a Tarski monster group for
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267:{\displaystyle N\trianglelefteq G}
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300:is any subgroup distinct from
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444:Ol'shanskiĭ, A. Yu. (1991),
403:{\displaystyle p>10^{75}}
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81:Alexander Yu. Olshanskii
293:{\displaystyle U\leq G}
481:-related article is a
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363:{\displaystyle p^{2}}
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43:Tarski monster group
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336:{\displaystyle NU}
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432:A. Yu. Olshanskii
313:{\displaystyle N}
241:{\displaystyle G}
219:{\displaystyle G}
191:{\displaystyle p}
171:{\displaystyle p}
151:{\displaystyle G}
131:{\displaystyle p}
68:of order a fixed
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70:prime number
66:cyclic group
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45:, named for
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526:Categories
426:References
202:Properties
198:elements.
114:Definition
370:elements.
285:≤
259:⊴
537:P-groups
106:and the
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88:-group
77:simple
477:This
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483:stub
450:ISBN
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274:and
118:Let
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256:N
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186:p
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62:G
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