A group G is called metacyclic if it contains a normal cyclic subgroup such that the quotient group of G is also cyclic. In this paper, we compute the size of centralizers of some non-abelian metacyclic 2-groups of negative type. Using these results, we obtain the set of conjugacy class lengths of these groups.
Topics
Group theory
REFERENCES
1.
A.R.
Camina
, R.D.
Camina
, The influence of conjugacy class sizes on the structure of finite groups: a survey
, Asian-Eur. J. Math.
4
(4
) (2011
) 559
–588
.2.
N.
Itô
, On finite groups with given conjugate type I
, Nagoya Math. J.
6
(1953
) 17
–28
.3.
N.
Itô
, On finite groups with given conjugate type II
, Osaka J. Math.
7
(1970
) 231
–251
.4.
S.
Dolfi
, E.
Jabara
, The structure of finite groups of conjugate rank 2
, Bull. London Math. Soc.
35
(2009
) 339
–344
.5.
A.
Ahmad
, S.
Magidin
, R.F.
Morse
, Two generator p-groups of nilpotency class 2
and their conjugacy classes, Publ. Math. Debrecen
81
(2012
) 145
–166
.6.
A.
Beltran
, M.J.
Felipe
, Some class size conditions implying solvability of finite groups
, J. Group Theory
9
(6
) (2006
) 787
–797
.7.
A.
Mann
, Some questions about p-groups
, J. Austral. Math. Soc. Ser. A
67
(3
) (1999
) 356
–379
.8.
X.
Liua
, Y.
Wangc
, H.
Wei
, Notes on the length of conjugacy classes of finite groups
, J. Pure Appl. Algebra
196
(2005
) 111
–117
.9.
J.R.
Beuerle
, An elementary classification of finite metacyclic p-groups of class at least three
, Algebra Colloq.
12
(2005
) 553
–562
.
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