Add to ORKGBy using tools from additive combinatorics, invariant theory and bounds on the size of the minimal generating sets of PSL2( q ), we prove the following growth property. There exists ɛ > 0 such that the following holds for any finite field q . Let G be the group SL2( q ), or PSL2( q ), and let A be a generating set of G. Then |A · A · A| ⩾ min {|A|1 +ɛ , |G|}. Our work extends the work of Helfgott [Helfgott, Ann. of Math. 167: 601-623, 2008] who proved similar results for the family {SL2( p ): p prime
AbstractLet p be a prime number and ℓ be any positive integer. Let G be the cyclic group of order pℓ...
AbstractA subset of a group is said to beproduct-freeif the product of two of its elements is never ...
AbstractEvery word w in the free group Fd defines for each group G a word map, also denoted w, from ...
AbstractThe diameter of a finite group G with respect to a generating set A is the smallest non-nega...
AbstractLet G be a finite abelian group of order g. We determine, for all 1⩽r,s⩽g, the minimal size ...
AbstractThe p-group generation algorithm from computational group theory is used to obtain informati...
AbstractLet G be a (topological) group. For 2⩽d∈N, denote by μd(G) the largest m for which there exi...
AbstractLet G be an abelian group of order n (written multiplicatively), let g∈G and let d be an int...
AbstractIf X is an n-element set, we call a family G⊂PX a k-generator for X if every x⊂X can be expr...
AbstractLet G be a group. We study the minimal sumset (or product set) size μG(r,s)=min{|A⋅B|}, wher...
AbstractIf n≥10, then there is a trivalent Cayley graph for G=PSL (n,q) whose diameter is O(log|G|)
AbstractGiven a group G and integers r and s, let μG(r,s) be the minimum cardinality of the product ...
AbstractWe produce examples in the cohomology of algebraic groups which answer two questions of Pars...
AbstractLet G be any of the groups (P)GL(n,q), (P)SL(n,q). Define a (simple) graph Γ=Γ(G) on the set...
AbstractLet G be a group and g1,…, gt a set of generators. There are approximately (2t − 1)n reduced...
AbstractLet p be a prime number and ℓ be any positive integer. Let G be the cyclic group of order pℓ...
AbstractA subset of a group is said to beproduct-freeif the product of two of its elements is never ...
AbstractEvery word w in the free group Fd defines for each group G a word map, also denoted w, from ...
AbstractThe diameter of a finite group G with respect to a generating set A is the smallest non-nega...
AbstractLet G be a finite abelian group of order g. We determine, for all 1⩽r,s⩽g, the minimal size ...
AbstractThe p-group generation algorithm from computational group theory is used to obtain informati...
AbstractLet G be a (topological) group. For 2⩽d∈N, denote by μd(G) the largest m for which there exi...
AbstractLet G be an abelian group of order n (written multiplicatively), let g∈G and let d be an int...
AbstractIf X is an n-element set, we call a family G⊂PX a k-generator for X if every x⊂X can be expr...
AbstractLet G be a group. We study the minimal sumset (or product set) size μG(r,s)=min{|A⋅B|}, wher...
AbstractIf n≥10, then there is a trivalent Cayley graph for G=PSL (n,q) whose diameter is O(log|G|)
AbstractGiven a group G and integers r and s, let μG(r,s) be the minimum cardinality of the product ...
AbstractWe produce examples in the cohomology of algebraic groups which answer two questions of Pars...
AbstractLet G be any of the groups (P)GL(n,q), (P)SL(n,q). Define a (simple) graph Γ=Γ(G) on the set...
AbstractLet G be a group and g1,…, gt a set of generators. There are approximately (2t − 1)n reduced...
AbstractLet p be a prime number and ℓ be any positive integer. Let G be the cyclic group of order pℓ...
AbstractA subset of a group is said to beproduct-freeif the product of two of its elements is never ...
AbstractEvery word w in the free group Fd defines for each group G a word map, also denoted w, from ...