On groups with a class-preserving outer automorphism

Involve

Volumn 7, Issue 2, 2014, Pages 171-179

  Brooksbank, Peter A ^a   Mizuhara, Matthew S ^a  

^a BUCKNELL UNIVERSITY   (United States)

Author keywords

class preserving automorphisms; p groups; polycyclic groups

Indexed keywords

EID: 84922021640     PISSN: 19444176     EISSN: 19444184     Source Type: Journal    
DOI: 10.2140/involve.2014.7.171     Document Type: Article

References (12)

1. [Bosma et al. 1997] W. Bosma, J. Cannon, and C. Playoust, “The Magma algebra system, I: The user language”, J. Symbolic Comput. 24:3–4 (1997), 235–265. MR 1484478 Zbl 0898.68039
2. [Burnside 1911] W. Burnside, Theory of groups of finite order, 2nd ed., Cambridge Univ. Press, New York, 1911. Reprinted Dover, New York, 1955. MR 16,1086c Zbl 0064.25105
3. [Burnside 1913] W. Burnside, “On the outer isomorphisms of a group”, Proc. London Math. Soc. S2-11:1 (1913), 40–42. MR 1577234 JFM 43.0198.03
4. [Eick and Leedham-Green 2008] B. Eick and C. Leedham-Green, “On the classification of prime-power groups by coclass”, Bull. Lond. Math. Soc. 40:2 (2008), 274–288. MR 2009b:20030 Zbl 1168.20007
5. [Feit and Seitz 1989] W. Feit and G. M. Seitz, “On finite rational groups and related topics”, Illinois J. Math. 33:1 (1989), 103–131. MR 90a:20016 Zbl 0701.20005
6. [Heineken 1979] H. Heineken, “Nilpotente Gruppen, deren sämtliche Normalteiler charakteristisch sind”, Arch. Math. (Basel) 33:6 (1979), 497–503. MR 81h:20023 Zbl 0413.20017
7. [Hertweck 2001] M. Hertweck, “Class-preserving automorphisms of finite groups”, J. Algebra 241:1 (2001), 1–26. MR 2002e:20047 Zbl 0993.20017
8. [Holt et al. 2005] D. F. Holt, B. Eick, and E. A. O’Brien, Handbook of computational group theory, Chapman & Hall, Boca Raton, FL, 2005. MR 2006f:20001 Zbl 1091.20001
9. [Malinowska 1992] I. Malinowska, “On quasi-inner automorphisms of a finite p–group”, Publ. Math. Debrecen 41:1–2 (1992), 73–77. MR 93g:20069 Zbl 0792.20019
10. [O’Brien 1990] E. A. O’Brien, “The p–group generation algorithm”, J. Symbolic Comput. 9:5–6 (1990), 677–698. MR 91j:20050 Zbl 0736.20001
11. [Wall 1947] G. E. Wall, “Finite groups with class-preserving outer automorphisms”, J. London Math. Soc. 22 (1947), 315–320. MR 10,8g Zbl 0030.00901
12. [Yadav 2011] M. K. Yadav, “Class preserving automorphisms of finite p–groups: a survey”, pp. 569–579 in Groups St Andrews 2009 (Bath, 2009), vol. II, edited by C. M. Campbell et al., London Math. Soc. Lecture Note Ser. 388, Cambridge Univ. Press, 2011. MR 2012j:20061 Zbl 1231.20024