Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-23T10:34:06.836Z Has data issue: false hasContentIssue false
  • English
  • Français

NONINNER AUTOMORPHISMS OF ORDER $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}p$ IN FINITE $p$-GROUPS OF COCLASS 2, WHEN $p>2$

Part of: Representation theory of groups

Published online by Cambridge University Press:  10 June 2014

S. FOULADI  and
R. ORFI
S. FOULADI
Affiliation:
Faculty of Mathematical Sciences and Computer, Kharazmi University, 50 Taleghani Ave., Tehran 1561836314, Iran email [email protected]
R. ORFI*
Affiliation:
Faculty of Mathematical Sciences and Computer, Kharazmi University, 50 Taleghani Ave., Tehran 1561836314, Iran email [email protected]
*
✉[email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

It is shown that if $G$ is a finite $p$-group of coclass 2 with $p>2$, then $G$ has a noninner automorphism of order $p$.

Keywords

automorphisms of p-groupsp-groups of coclass 2noninner automorphismsderivations

MSC classification

Secondary: 20D45: Automorphisms 20D15: Nilpotent groups, $p$-groups
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 90 , Issue 2 , October 2014 , pp. 232 - 236
Copyright
Copyright © 2014 Australian Mathematical Publishing Association Inc. 

References

Abdollahi, A., ‘Finite p-groups of class 2 have noninner automorphisms of order p’, J. Algebra 312 (2007), 876–879.Google Scholar
Abdollahi, A., ‘Powerful p-groups have non-inner automorphisms of order p and some cohomology’, J. Algebra 323 (2010), 779–789.CrossRefGoogle Scholar
Abdollahi, A., Ghoraishi, M. and Wilkens, B., ‘Finite p-groups of class 3 have noninner automorphisms of order p’, Beitr. Algebra Geom. 54 (2013), 363–381.CrossRefGoogle Scholar
Adney, J. E. and Yen, T., ‘Automorphisms of a p-group’, Illinois J. Math. 9 (1965), 137–143.Google Scholar
Blackburn, N., ‘On a special class of p-groups’, Acta Math. 100 (1958), 45–92.Google Scholar
Bodnarchuk, L. Yu. and Pilyavska, O. S., ‘On the existence of a noninner automorphism of order p for p groups’, Ukrainian Math. J. 53 (2001), 1771–1783.Google Scholar
Deaconescu, M. and Silberberg, G., ‘Noninner automorphisms of order p of finite p-groups’, J. Algebra 250 (2002), 283–287.Google Scholar
Eick, B. and Leedham-Green, C. R., ‘On the classification of prime-power groups by coclass’, Bull. Lond. Math. Soc. 40 (2008), 274–288.Google Scholar
Gaschütz, W., ‘Nichtabelsche p-Gruppen besitzen äussere p-Automorphismen’, J. Algebra 4 (1966), 1–2.Google Scholar
Jamali, A. R. and Viseh, M., ‘On the existence of noninner automorphisms of order two in finite 2-groups’, Bull. Aust. Math. Soc. 87 (2013), 278–287.Google Scholar
Leedham-Green, C. R. and Newman, M. F., ‘Space groups and groups of prime-power order. I’, Arch. Math. (Basel) 35 (1980), 193–202.Google Scholar
Liebeck, H., ‘Outer automorphisms in nilpotent p-groups of class 2’, J. Lond. Math. Soc. 40 (1965), 268–275.Google Scholar
Mazurov, V. D. and Khukhro, E. I. (eds.) \unskip , Unsolved Problems in Group Theory, The Kourovka Notebook, 16 (Russian Academy of Sciences, Siberian Division, Institute of Mathematics, Novosibirsk, 2006).Google Scholar
Newman, M. F., ‘On coclass and trivial Schur multiplicator’, J. Algebra 322 (2009), 910–913.Google Scholar
Newman, M. F. and O’Brien, E. A., ‘Classifying 2-groups by coclass’, Trans. Amer. Math. Soc. 351 (1999), 131–169.CrossRefGoogle Scholar
Schmid, P., ‘Normal p-subgroups in the group of outer automorphisms of a finite p-group’, Math. Z. 147 (1976), 271–277.CrossRefGoogle Scholar
Shabani Attar, M., ‘On a conjecture about automorphisms of finite p-groups’, Arch. Math. (Basel) 93 (2009), 399–403.Google Scholar
The GAP Group, GAP—Groups, Algorithms, and Programming, Version 4.4.12.http://www.gap-system.org.Google Scholar