Affiliation:
1. Department of Mathematics , University of Brasília , Brasília - DF 70910-900 , Brazil
Abstract
Abstract
Let q be a prime and A a finite q-group of exponent q acting by automorphisms on a finite
q
′
{q^{\prime}}
-group G.
Assume that A has order at least
q
3
{q^{3}}
.
We show that if
γ
∞
(
C
G
(
a
)
)
{\gamma_{\infty}(C_{G}(a))}
has order at most m for any
a
∈
A
#
{a\in A^{\#}}
, then the order of
γ
∞
(
G
)
{\gamma_{\infty}(G)}
is bounded solely in terms of m.
If the Fitting subgroup of
C
G
(
a
)
{C_{G}(a)}
has index at most m for any
a
∈
A
#
{a\in A^{\#}}
, then the second Fitting subgroup of G has index bounded solely in terms of m.
Subject
Algebra and Number Theory
Reference13 articles.
1. C. Acciarri, P. Shumyatsky and D. Silveira,
Engel sinks of fixed points in finite groups,
J. Pure Appl. Algebra 223 (2019), no. 11, 4592–4601.
2. C. Acciarri, P. Shumyatsky and A. Thillaisundaram,
Conciseness of coprime commutators in finite groups,
Bull. Aust. Math. Soc. 89 (2014), 252–258.
3. E. de Melo, A. S. Lima and P. Shumyatsky,
Nilpotent residual of fixed points,
Arch. Math. 111 (2018), 13–21.
4. E. de Melo and P. Shumyatsky,
Finite groups and their coprime automorphisms,
Proc. Amer. Math. Soc. 145 (2017), 3755–3760.
5. E. de Melo and P. Shumyatsky,
Fitting subgroup and nilpotent residual of fixed points,
Bull. Aust. Math. Soc., to appear.
Cited by
2 articles.
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