Coclass theory



Bettina Eick




Coclass theory has been one of my main research projects for many years. It started as an approach towards a new classification for finite p-groups. Meanwhile, similar ideas has been tried for nilpotent Lie algebras and nilpotent associative algebras. Below are my main publications in these areas.


Coclass Theory for finite p-Groups
  • On the classification of prime-power groups by coclass. With Charles Leedham-Green. Bull. Lond. Math. Soc. 40, 274 -- 288 (2008)
  • On the classification of groups of prime-power order by coclass: The 3-groups of coclass 2. With C.R. Leedham-Green, M.F. Newman and E.A. O'Brien. J. Algebra Comput. 23, 1243 -- 1288 (2013).
  • On the number of infinite branches in the graph of all p-groups of coclass r. J. Group Theory 8, 687 - 700 (2005)
  • On the determination of the uniserial space groups with a given coclass. J. London Math. Soc. (2) 71, 622 - 642 (2005)
  • Schur multiplicators of finite p-groups with fixed coclass. Israel J. Math. 166, 157 -- 166 (2008)
  • Schur multiplicators of infinite pro-p-groups with finite coclass. Israel J. Math. 166, 147 -- 156 (2008)
  • Automorphism groups of 2-groups. J. Algebra (Comput. Sec.) 300, 91 -- 101 (2006)
  • On p-groups of maximal class with 'large' automorphism group. With H. Dietrich. J. Group Theory 20, 227 -- 256 (2017).
  • Metabelian p-groups and coclass theory J. Algebra 421, 102 -- 118 (2014).
  • Computation of low-dimensional (co)homology groups for infinite sequences of p-groups with fixed coclass. With D. Feichtenschlager. IJAC 21(4), 635--649 (2011)
  • Investigating p-groups by coclass with GAP. With H. Dietrich and D. Feichtenschlager. In Proceedings `AMS Special Session on Computational Group Theory' by Kappe, Magidin and Morse, AMS Contemp. Math. 470, 45 -- 61 (2008)
  • Cochain sequences and the Quillen category of a coclass family. With D. Green. J. Australian Math. Soc. 102, 185 -- 204 (2017)
  • The Quillen categories of $p$-groups and coclass theory. With D. Green. Israel J. Math. 206, 183 -- 212 (2015).
  • The class-breadth conjecture revisited. With M. Newman and E.A.O'Brien J. Algebra 300, 384 -- 393 (2006).
  • On efficient presentations for infinite families of 2-groups with fixed coclass. With H. Abdolzadeh. Algebra Colloquium 20, 561 -- 572 (2013).
Coclass Theory for Nilpotent Associative Algebras
  • Classifying nilpotent associative algebras: small coclass and finite fields. With T. Moede. In Proceedings: Algorithmic and experimental methods in algebra, geometry, and number theory. Springer (ISBN 978-3-319-70565-1 and 978-3-319-70566-8), 213 -- 229 (2017).
  • Coclass theory for finite nilpotent associative algebras: Algorithms and a periodicity conjecture. With T. Moede. Exp. Math. 26, 267 -- 274 (2017)
  • Nilpotent associative algebras and coclass theory. With T. Moede. J. Algebra 434, 249 -- 260 (2015)
  • Coclass theory for nilpotent semigroups via their associated algebras. With Andreas Distler. J. Algebra 373, 491 -- 501 (2013).