Geodesic
Finite $p$-Groups with Automorphism of a Special Form
Algebra i logika, Tome 45 (2006) no. 4, pp. 379-389.

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Research on finite solvable groups with $C$-closed invariant subgroups has given rise to groups structured as follows. Let $p,q_1,q_2,\dots,q_m$ be distinct primes, $n_i$ be the exponent of $p$ modulo $q_i$, and $n$ be the exponent of $p$ modulo $r=\prod\limits_{i=1}^m q_i$. Then $G=P\lambda\langle x\rangle$, where $P$ is a group and $Z(P)=P'=\prod\limits_{i=1}^{m}Z_i$; here, $Z_i$ and $P/Z(P)$ are elementary Abelian groups of respective orders $p^{n_i}$ and $p^n$, $|x|=r$, the element $x$ acts irreducibly on $P/Z(P)$ and on each of the subgroups $Z_i$, and $C_P(x^{q_i})=Z_i$. We state necessary and sufficient conditions for such groups to exist.
Mots-clés : automorphism
Keywords: finite $p$-group. 
@article{AL_2006_45_4_a0,
     author = {V. A. Antonov and S. G. Chekanov},
     title = {Finite $p${-Groups} with {Automorphism} of a {Special} {Form}},
     journal = {Algebra i logika},
     pages = {379--389},
     publisher = {mathdoc},
     volume = {45},
     number = {4},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2006_45_4_a0/}
}
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V. A. Antonov; S. G. Chekanov. Finite $p$-Groups with Automorphism of a Special Form. Algebra i logika, Tome 45 (2006) no. 4, pp. 379-389. http://geodesic.mathdoc.fr/item/AL_2006_45_4_a0/

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