Abstract. We discuss the structure of the local error of exponential operator splitting methods. In particular, it is shown that the leading error term is a Lie element, i.e., a linear combination of higher-degree commutators of the given operators. This structural assertion can be used to formulate a simple algorithm for the automatic generation of a minimal set of polynomial equations representing the order conditions, for the general case as well as in symmetric settings.
A proper subgroup M of a group G is called a CC-subgroup of G if the centralizer C G ðmÞ of every m 2 M # ¼ M nf1g is contained in M. In this paper we classify all finite groups containing a CC-subgroup, extending work of many authors.
We fill details in the proof of [HZ, Lemma 13] (that is [4, Lemma 3.2]). For easier reading we include the relevant part of section 3 ibidem. 20E18 (primary), 20E06, 22C05 (secondary).
HNN-embeddingWe introduce a notion of a pro-p HNN-group as a generalization of pro-p HNNextension in the sense of [1, page 97]. It also can be defined as a sequence of pro-p HNN-extensions. During the definition to follow, i belongs to a finite set I of indices.
Motivated by a well-known conjecture of Andrews and Curtis, we consider the question as to how in a given n-generator group G, a given set of n “annihilators” of G, that is, with normal closure all of G, can be transformed by standard moves into a generating n-tuple. The recalcitrance of G is defined to be the least number of elementary standard moves (”elementary M-transformations”) by means of which every annihilating n-tuple of G can be transformed into a generating n-tuple. We show that in the classes of finite and soluble groups, having zero recalcitrance is equivalent to nilpotence, and that a large class of 2-generator soluble groups has recalcitrance at most 3. Some examples and remarks are included.
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