Finite p-groups with automorphism of a special form |
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Authors: | V A Antonov S G Chekanov |
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Institution: | (1) éngel’sa, 44-B, 57, Chelyabinsk, 654080, Russia;(2) Solnechnaya, 12-A, 34, Chelyabinsk, 654014, Russia |
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Abstract: | Research on finite solvable groups with C-closed invariant subgroups has given rise to groups structured as follows. Let p,
q1, q2, ..., qm be distinct primes, ni be the exponent of p modulo qi, and n be the exponent of p modulo
. Then G = Pλ〈x〉, where P is a group and
; Zi; here, Zi and P/Z(P) are elementary Abelian groups of respective orders
and pn, |x| = r, the element x acts irreducibly on P/Z(P) and on each of the subgroups Zi, and
. We state necessary and sufficient conditions for such groups to exist.
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Translated from Algebra i Logika, Vol. 45, No. 4, pp. 379–389, July–August, 2006. |
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Keywords: | automorphism finite p-group |
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