On $p$-complements of finite groups
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 10 (2013), pp. 414-417
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A subgroup $H$ of a finite group $G$ is called a $p$-complement for a prime $p$, if the order of $H$ is not divided by $p$ and the index $|G:H|$ is a power of $p$. We give examples of a finite group that possesses two nonisomorphic $p$-complements and of a finite group in which all $p$-complements are isomorphic but not conjugate in the automorphism group.
Keywords:
finite group
Mots-clés : $p$-complement.
Mots-clés : $p$-complement.
@article{SEMR_2013_10_a10,
author = {A. A. Buturlakin and D. O. Revin},
title = {On $p$-complements of finite groups},
journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
pages = {414--417},
year = {2013},
volume = {10},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SEMR_2013_10_a10/}
}
A. A. Buturlakin; D. O. Revin. On $p$-complements of finite groups. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 10 (2013), pp. 414-417. http://geodesic.mathdoc.fr/item/SEMR_2013_10_a10/
[1] P. Hall, “A note on soluble groups”, J. London Math. Soc., 3 (1928), 98–105 | DOI | MR | Zbl
[2] P. Hall, “A characteristic property of soluble groups”, J. London Math. Soc., 12 (1937), 198–200 | DOI | MR
[3] S. A. Chunikhin, “On soluble groups”, Isv. NIIMM Tom. Univ., 2 (1938), 220–223 (in Russian) | Zbl
[4] I. M. Isaacs, Finite group theory, AMS, Providence, RI, 2008 | MR
[5] Z. Arad, E. Fisman, “On finite factorizable groups”, J. Algebra, 86 (1984), 522–548 | DOI | MR | Zbl
[6] Z. Arad, M. B. Ward, “New criteria for the solvability of finite groups”, J. Algebra, 77 (1982), 234–246 | DOI | MR | Zbl