臺灣博碩士論文加值系統

A finite group is said to be power-commutative ($PC$) if the commutativity of nontrivial powers of
two elements implies the commutativity of the two elements. We study irreducible characters of finite solvable
$PC$-groups of first type and related problems to the Taketa's inequality in this article.

1 Abstract
2 Introduction
3 Basic Properties of Finite Solvable PC-group
4 Irreducible Characters of Finite Solvable PC-groups of First Type
5 Studies on Normally Monomial Groups
6 Further Research
A Proof of Lemma 5.5

Y.F. Wu, On locally finite power-commutativity
groups, J. Group Theory 3 (2000), 57--65.

D. J. S. Robinson, A Course in the Theory
of Groups, Spriner-Verlag, 1980.

B. Huppert, Character Theory of Finite Groups, de Gruyter, 1998.

B. Huppert and N. Blackburn, Finite Groups II, Springer-Verlag, 1982.

N. H. Lai, Finite Groups With Elements Of Prime Order, Department of Mathematics National University of Singapore, (1990-1991).

D. Wilkinson, The Groups of Exponent $p$ and Order $p^7$ ($p$ Any Prime), J. Algebra 118 (1988), 109--119.

I. M. Issacs, Character Theory of Finite Groups, Acaddemic. Press, 1976.

T. M. Keller, D. Ragan, and G. T. Tims, On the Taketa bound for normally monomial $p$-groups of maximal class, J. Algebra 277 (2004), 675--688.

L. D. Maritino and M. C. Tamburini, Some Remarks on the Degrees of Faithful Irreducible Representations of a Finite $p$-Group, Geometriae Dedicata 41 (1992), 155--164.

T. Berger, Characters and derived length in groups of odd
order, J. Algebra 39 (1976), 199--207.