منابع مشابه
CHAPTER IV Groups and Group Actions
This chapter develops the basics of group theory, with particular attention to the role of group actions of various kinds. The emphasis is on groups in Sections 1–3 and on group actions starting in Section 6. In between is a two-section digression that introduces rings, fields, vector spaces over general fields, and polynomial rings over commutative rings with identity. Section 1 introduces gro...
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In this note we introduce the notion of a group action on a set and use it to prove a number of theorems about p-groups and the Sylow theorems. For undefined terms see any decent book on group theory. The theory of p-groups and the Sylow theorems have a number of applications in Galoistheory. The nice structure of p-groups will translate via the fundamental theorem of Galois theory to nice stru...
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Let G be a reductive linear algebraic group, P a parabolic subgroup of G and Pu its unipotent radical. We consider the adjoint action of P on the Lie algebra pu of Pu. Richardson’s dense orbit theorem says that there is a dense P -orbit in pu. We consider some instances when P acts with a dense orbit on terms p u of the descending central series of pu. In particular, we show (in good characteri...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 1971
ISSN: 0001-8708
DOI: 10.1016/0001-8708(71)90018-1