Add to ORKGWe obtain a classification of the finite two-generated cyclic-by-abelian groups of prime-power order. For that we associate to each such group $G$ a list $\inv(G)$ of numerical group invariants which determines the isomorphism type of $G$. Then we describe the set formed by all the possible values of $\inv(G)$. This allows computer implementations for constructing all the finite-two generated cyclic-by-abelian groups of a given prime-power order, computing the invariants of such a group, and to decide whether two such groups are isomorphic.Comment: 27 pages. Updated reference
AbstractLet F be a finite group with a Sylow 2-subgroup S that is normal and abelian. Using hyperele...
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Description of automorphism groups of non-metacyclic minimal nonabelian finite p-groups with p>2 in ...
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AbstractLet F be a finite group with a Sylow 2-subgroup S that is normal and abelian. Using hyperele...
Let E be a elementary abelian p-group of order q = p^n. Let W be a faithful indecomposable represent...
Description of automorphism groups of non-metacyclic minimal nonabelian finite p-groups with p>2 in ...
Let $p$ be a an odd prime and let $G$ be a finite $p$-group with cyclic commutator subgroup $G'$. We...
AbstractFor odd primes we prove some structure theorems for finite p-groups G, such that G″≠1 and |G...
AbstractThe isomorphism problem for groups is to determine whether two finite groups are isomorphic....
Let $p$ be an odd prime number. We show that the modular isomorphism problem has a positive answer f...
AbstractFor any finite group G, let Ω(G) denote the Burnside ring of G. Let A denote the class of fi...
AbstractIn this paper, we shall verify the conjecture |Z1(A,G)|≡0(modgcd(|A/A′|,|G|)) of [T. Asai, T...
We show that elementary abelian direct factors can be disregarded in the study of the modular isomor...
AbstractThe power graph of a group is the graph whose vertex set is the group, two elements being ad...
We study the Modular Isomorphism Problem applying a combination of existing and new techniques. We m...
AbstractIf G is any finite Abelian group defineγ(G)=∑i(ei−1)where ei are the canonic invariants of G...
AbstractFor a finite group G and a set I ⊆ {1, 2,…, n} let G(n,I) = ∑g ∈ G ε1(g)⊗ε2(g)⊗⋯⊗εn(g),where...
AbstractThe paper classifies (up to isomorphism) those groups of prime power order whose derived sub...
AbstractLet F be a finite group with a Sylow 2-subgroup S that is normal and abelian. Using hyperele...
Let E be a elementary abelian p-group of order q = p^n. Let W be a faithful indecomposable represent...
Description of automorphism groups of non-metacyclic minimal nonabelian finite p-groups with p>2 in ...