Matches in SemOpenAlex for { <https://semopenalex.org/work/W2766996820> ?p ?o ?g. }
Showing items 1 to 91 of
91
with 100 items per page.
- W2766996820 abstract "This paper concerns finite groups of class (at most) two and of odd prime exponent $p$. Such a group is called special if the center lies within its derived group. Every group of class 2 and exponent $p$ can be uniquely expressed as the direct product of an elementary abelian group and a special group. This reduces the isomorphism problem to special groups. The special groups having $G'$ cyclic are well known. Groups having $|G'|=p^2$ are known to be generated by two abelian subgroups. As such, they can be described by a pair of Scharlau Matrices which we will define. Using these, Vishnevetskii ([1], [2]) classified the special groups which are not central products of groups of smaller order. We call these Vishnevetskii indecomposable. All decomposable groups are central products of two or more indecomposable groups. By Theorem 2 of [2], if $G$ is a special group with derived group of order $p^2$ then the indecomposable central factors of $G$, together with their multiplicities, form a set of invariants for $G$. However these invariants do not determine $G$, since (as we will show below) two nonisomorphic groups can have the same indecomposable central factors. The groups of exponent $p$ and order dividing $p^8$ are already in the literature. In this paper we prove that there are six isomorphism types of special groups of order $p^9$ having $|G'|=p^2$, and we list them. We will also introduce a way of representing groups of class 2 having exponent $p$ by using digraphs with flows on the edges. The digraph is compact and gives, on sight, a great deal of structural information about the group and completely defines the group. Some group invariants will also be described which are easy to compute from the digraphs and which can readily be used to distinguish the isomorphism types for small orders." @default.
- W2766996820 created "2017-11-10" @default.
- W2766996820 creator A5091269548 @default.
- W2766996820 date "2017-10-15" @default.
- W2766996820 modified "2023-09-27" @default.
- W2766996820 title "Groups of order $p^9$, class 2, and exponent $p$ having derived group of order $p^2$" @default.
- W2766996820 cites W2002679650 @default.
- W2766996820 hasPublicationYear "2017" @default.
- W2766996820 type Work @default.
- W2766996820 sameAs 2766996820 @default.
- W2766996820 citedByCount "1" @default.
- W2766996820 countsByYear W27669968202019 @default.
- W2766996820 crossrefType "posted-content" @default.
- W2766996820 hasAuthorship W2766996820A5091269548 @default.
- W2766996820 hasConcept C10138342 @default.
- W2766996820 hasConcept C114614502 @default.
- W2766996820 hasConcept C115624301 @default.
- W2766996820 hasConcept C118615104 @default.
- W2766996820 hasConcept C121332964 @default.
- W2766996820 hasConcept C136170076 @default.
- W2766996820 hasConcept C138885662 @default.
- W2766996820 hasConcept C154945302 @default.
- W2766996820 hasConcept C157480366 @default.
- W2766996820 hasConcept C162324750 @default.
- W2766996820 hasConcept C170124329 @default.
- W2766996820 hasConcept C182306322 @default.
- W2766996820 hasConcept C185592680 @default.
- W2766996820 hasConcept C203436722 @default.
- W2766996820 hasConcept C20725272 @default.
- W2766996820 hasConcept C2524010 @default.
- W2766996820 hasConcept C2777212361 @default.
- W2766996820 hasConcept C2780388253 @default.
- W2766996820 hasConcept C2781311116 @default.
- W2766996820 hasConcept C33923547 @default.
- W2766996820 hasConcept C41008148 @default.
- W2766996820 hasConcept C41895202 @default.
- W2766996820 hasConcept C62520636 @default.
- W2766996820 hasConcept C8010536 @default.
- W2766996820 hasConcept C90673727 @default.
- W2766996820 hasConceptScore W2766996820C10138342 @default.
- W2766996820 hasConceptScore W2766996820C114614502 @default.
- W2766996820 hasConceptScore W2766996820C115624301 @default.
- W2766996820 hasConceptScore W2766996820C118615104 @default.
- W2766996820 hasConceptScore W2766996820C121332964 @default.
- W2766996820 hasConceptScore W2766996820C136170076 @default.
- W2766996820 hasConceptScore W2766996820C138885662 @default.
- W2766996820 hasConceptScore W2766996820C154945302 @default.
- W2766996820 hasConceptScore W2766996820C157480366 @default.
- W2766996820 hasConceptScore W2766996820C162324750 @default.
- W2766996820 hasConceptScore W2766996820C170124329 @default.
- W2766996820 hasConceptScore W2766996820C182306322 @default.
- W2766996820 hasConceptScore W2766996820C185592680 @default.
- W2766996820 hasConceptScore W2766996820C203436722 @default.
- W2766996820 hasConceptScore W2766996820C20725272 @default.
- W2766996820 hasConceptScore W2766996820C2524010 @default.
- W2766996820 hasConceptScore W2766996820C2777212361 @default.
- W2766996820 hasConceptScore W2766996820C2780388253 @default.
- W2766996820 hasConceptScore W2766996820C2781311116 @default.
- W2766996820 hasConceptScore W2766996820C33923547 @default.
- W2766996820 hasConceptScore W2766996820C41008148 @default.
- W2766996820 hasConceptScore W2766996820C41895202 @default.
- W2766996820 hasConceptScore W2766996820C62520636 @default.
- W2766996820 hasConceptScore W2766996820C8010536 @default.
- W2766996820 hasConceptScore W2766996820C90673727 @default.
- W2766996820 hasLocation W27669968201 @default.
- W2766996820 hasOpenAccess W2766996820 @default.
- W2766996820 hasPrimaryLocation W27669968201 @default.
- W2766996820 hasRelatedWork W13275624 @default.
- W2766996820 hasRelatedWork W1524382115 @default.
- W2766996820 hasRelatedWork W1831664562 @default.
- W2766996820 hasRelatedWork W1976642851 @default.
- W2766996820 hasRelatedWork W2038328103 @default.
- W2766996820 hasRelatedWork W2056724227 @default.
- W2766996820 hasRelatedWork W2060668733 @default.
- W2766996820 hasRelatedWork W2066574945 @default.
- W2766996820 hasRelatedWork W2156699998 @default.
- W2766996820 hasRelatedWork W2169076938 @default.
- W2766996820 hasRelatedWork W2313029091 @default.
- W2766996820 hasRelatedWork W2319831419 @default.
- W2766996820 hasRelatedWork W2322831583 @default.
- W2766996820 hasRelatedWork W2887914726 @default.
- W2766996820 hasRelatedWork W2950123706 @default.
- W2766996820 hasRelatedWork W3104939203 @default.
- W2766996820 hasRelatedWork W3146039763 @default.
- W2766996820 hasRelatedWork W3196980628 @default.
- W2766996820 hasRelatedWork W2277701423 @default.
- W2766996820 hasRelatedWork W3146697923 @default.
- W2766996820 isParatext "false" @default.
- W2766996820 isRetracted "false" @default.
- W2766996820 magId "2766996820" @default.
- W2766996820 workType "article" @default.