Read e-book online Algebraic Topology and Tranformation Groups PDF

By Tammo tom Dieck

This publication is a jewel– it explains vital, beneficial and deep themes in Algebraic Topology that you simply won`t locate in different places, conscientiously and in detail."""" Prof. Günter M. Ziegler, TU Berlin

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Additional resources for Algebraic Topology and Tranformation Groups

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The fact that a group G is in vC is also expressed by saying that G is virtually C or that G is virtually in C. Clearly, a group has all the virtual properties possessed by any of its finite extensions and its subgroups of finite index. For classes that contain the trivial group and are closed with respect to isomorphisms, extensions and taking subgroups of finite index, Schneebeli [Sch] studied the question as to when vC is extension closed. His results apply to certain one-relator groups, so we recount them, after first reviewing some general ideas about extensions.

Notice that p is the biggest prime dividing I5I. 25), Projb(S) is the set of all maximal it -subgroups of S. With similar arguments to those used in BALLESTER-BOLINCHES, EZQUERRO: SATURATION OF FORMATIONS 31 step 4, we prove that the prime p cannot exist and therefore Sj is of full characteristic. 0 Conjecture. Let Sj be a saturated formation with (1) # Sj # 4E. Then the following statements are equivalent: i) For every saturated formation 3, the formation $ f ii) S5 =' for some prime p. 1' is saturated.

Throughout this section we assume that our one-relator groups are finitely generated. 1. Let G be a virtually one-relator group and H a one-relator group of finite index in G. Then (1) G is virtually torsion free. (2) If rank H > 3 then G contains a subgroup of finite index which maps epimorphically onto a free group of rank 2. In particular, in this case G is SQ-universal. (3) G has finite cohomological dimension. BENCSATH, FINE: VIRTUALLY ONE-RELATOR GROUPS 46 (4) If H has non-trivial center then G has a non-trivial center.

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Algebraic Topology and Tranformation Groups by Tammo tom Dieck


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