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Finite soluble groups containing an element of prime order whose centralizer is small (1981)

Hartley, B. ; Meixner, T.

Springer

Archiv der Mathematik 36 (1981), S. 211-213

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ISSN: 1420-8938

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract In [2] we proved that ifG is a finite group containing an involution whose centralizer has order bounded by some numberm, thenG contains a nilpotent subgroup of class at most two and index bounded in terms ofm. One of the steps in the proof of that result was to show that ifG is soluble, then ¦G/F(G) ¦ is bounded by a function ofm, where F (G) is the Fitting subgroup ofG. We now show that, in this part of the argument, the involution can be replaced by an arbitrary element of prime order.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01223692

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