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The automorphism group for p-central p-groups | ||
| International Journal of Group Theory | ||
| مقاله 6، دوره 1، شماره 2، شهریور 2012، صفحه 59-71 اصل مقاله (328.57 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2012.745 | ||
| نویسنده | ||
| Anitha Thillaisundaram* | ||
| University of Cambridge, UK | ||
| چکیده | ||
| A $p$-group $G$ is $p$-central if $G^{p}\le Z(G)$, and $G$ is $p^{2}$-abelian if $(xy)^{p^{2}}=x^{p^{2}}y^{p^{2}}$ for all $x,y\in G$. We prove that for $G$ a finite $p^{2}$-abelian $p$-central $p$-group, excluding certain cases, the order of $G$ divides the order of $\text{Aut}(G)$. | ||
| کلیدواژهها | ||
| automorphism group؛ $p$-central؛ $(p^2)$-abelian | ||
| مراجع | ||
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J. Buckley (1975) Automorphism groups of isoclinic
$p$-groups J. London Math. Soc. (2) 12, 37-44
R. M. Davitt (1972) The automorphism group of finite
$p$-abelian $p$-groups Illinois J. Math. 16, 76-85
R. M. Davitt (1980) On the automorphism group of a
finite $p$-group with a small central quotient Canad. J. Math. 32, 1168-1176
R. M. Davitt \& A. D. Otto (1972) On the automorphism
group of a finite modular $p$-group Proc. Amer. Math. Soc. 35 (2), 399-404
R. M. Davitt \& A. D. Otto (1971) On the automorphism
group of a finite $p$-group with the central quotient metacyclic Proc. Amer. Math. Soc. 30 (3), 467-472
T. Exarchakos (1989) On $p$-groups of small order Publ. Inst. Math. (Beograd) (N. S.) (59) 45, 73-76
R. Faudree (1968) A note on the automorphism group
of a $p$-group Proc. Amer. Math. Soc. 19, 1379-1382
S. Fouladi, A. R. Jamali \& R. Orfi (2007) Automorphism
groups of finite $p$-groups of coclass 2 J. Group Theory 10 (4), 437-440
W. Gasch\"{u}tz (1966) Nichtabelsche $p$-Gruppen
besitzen \"{a}ussere $p$-Automorphismen (German) J. Algebra 4, 1-2
N. Gavioli (1993) The number of automorphisms of groups
of order $p^{7}$ Proc. Roy. Irish Acad. Sect. 93 (2), 177-184
C. J. Hillar \& D. L. Rhea (2007) Automorphisms of
finite abelian groups Amer. Math. Monthly 114 (10), 917-923
K. G. Hummel (1975) The order of the automorphism
group of a central product Proc. Amer. Math. Soc. 47 (1), 37-40
C. R. Leedham-Green \& S. McKay (2002) The Structure
of Groups of Prime Power Order London Mathematical Society
Monographs New Series, Oxford Science Publications 27
A. D. Otto (1966) Central automorphisms of a finite
$p$-group Trans. Amer. Math. Soc. 125, 280-287
I. B. S. Passi, M. Singh \& M. K. Yadav (2010) Automorphisms
of abelian group extensions J. Algebra (4) 324, 820-830
A. Ranum (1907) The group of classes of congruent
matrices with application to the group of isomorphisms of any
abelian group Trans. Amer. Math. Soc. 8, 71-91
A. Thillaisundaram (2011) PhD Thesis University of
Cambridge, UK
M. K. Yadav (2007) On automorphisms of finite $p$-groups J. Group Theory 10 (6), 859-866
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