We show that the number of factorizations \_=/ 1 } } } / r of a cycle of length n into a product of cycles of lengths a 1 , ..., a r , with r j=1 (a j &1)=n&1, is equal to n r&1 . This generalizes a well known result of J. Denes, concerning factorizations into a product of transpositions. We investi
โฆ LIBER โฆ
On infinite centralizers of groups
โ Scribed by V. P. Shunkov
- Publisher
- Springer US
- Year
- 1974
- Tongue
- English
- Weight
- 143 KB
- Volume
- 13
- Category
- Article
- ISSN
- 0002-5232
No coin nor oath required. For personal study only.
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The main result of the paper is the following theorem. Let G be a locally finite group containing a finite p-subgroup A such that C G A is finite and a non-cyclic subgroup B of order p 2 such that C G b has finite exponent for all b โ B # . Then G is almost locally solvable and has finite exponent.
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