COMPONENTS AND MINIMAL NORMAL SUBGROUPS OF FINITE AND PSEUDOFINITE GROUPS
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AbstractIt is proved that there is a formula$\pi \left( {h,x} \right)$in the first-order language of group theory such that each component and each non-abelian minimal normal subgroup of a finite groupGis definable by$\pi \left( {h,x} \right)$for a suitable elementhofG; in other words, each such subgroup has the form$\left\{ {x|x\pi \left( {h,x} \right)} \right\}$for someh. A number of consequences for infinite models of the theory of finite groups are described.
2009 ◽
Vol 74
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pp. 1429-1435
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1975 ◽
Vol 19
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pp. 257-262
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1953 ◽
Vol 5
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pp. 477-497
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1969 ◽
Vol 21
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pp. 418-429
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2014 ◽
Vol 57
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pp. 648-657
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2016 ◽
Vol 16
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pp. 1750160
2010 ◽
Vol 89
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pp. 1-7
1969 ◽
Vol 10
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pp. 359-362