## Abstract Let __G__ be a __p__ βgroup of maximal class of order __p__^__m__^ , __p__ β 2, and __c__ (__G__) the degree of commutativity of __G__. Let __c__~0~ be the nonnegative residue of __c__ modulo __p__ β 1. In this paper, by using only Lie algebra techniques, we prove that 2__c β₯ m__ β 2__p
The Exact Lower Bound for the Degree of Commutativity of a p-Group of Maximal Class
β Scribed by G.A. Fernandezalcober
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 286 KB
- Volume
- 174
- Category
- Article
- ISSN
- 0021-8693
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π SIMILAR VOLUMES
For a finite group G, let k G denote the number of conjugacy classes of G. We prove that a simple group of Lie type of untwisted rank l over the field of q Ε½ . l elements has at most 6 q conjugacy classes. Using this estimate we show that for Ε½ . Ε½ . 10 n completely reducible subgroups G of GL n, q
## Abstract We show that every 1βtough graph __G__ on __n__ β₯ 3 vertices with Ο~3~β§ __n__ has a cycle of length at least min{__n, n__ + (Ο~3~/3 ) β Ξ± + 1}, where Ο~3~ denotes the minimum value of the degree sum of any 3 pairwise nonadjacent vertices and Ξ± the cardinality of a miximum independent se