Matches in SemOpenAlex for { <https://semopenalex.org/work/W2912996409> ?p ?o ?g. }
Showing items 1 to 74 of
74
with 100 items per page.
- W2912996409 abstract "Denote by $G$ a finite group and let $psi(G)$ denote the sum of element orders in $G$. In 2009, H.Amiri, S.M.Jafarian Amiri and I.M.Isaacs proved that if $|G|=n$ and $G$ is non-cyclic, then $psi(G)<psi(C_n)$, where $C_n$ denotes the cyclic group of order $n$. In 2018 we proved that if $G$ is non-cyclic group of order $n$, then $psi(G)leq frac 7{11}psi(C_n)$ and equality holds if $n=4k$ with $(k,2)=1$ and $G=(C_2times C_2)times C_k$. In this paper we proved that equality holds if and only if $n$ and $G$ are as indicated above. Moreover we proved the following generalization of this result: Theorem 4. Let $q$ be a prime and let $G$ be a non-cyclic group of order $n$, with $q$ being the least prime divisor of $n$. Then $psi(G)leq frac {((q^2-1)q+1)(q+1)}{q^5+1}psi(C_n)$, with equality if and only if $n=q^2k$ with $(k,q)=1$ and $G=(C_qtimes C_q)times C_k$. Notice that if $q=2$, then $frac {((q^2-1)q+1)(q+1)}{q^5+1}=frac 7{11}$." @default.
- W2912996409 created "2019-02-21" @default.
- W2912996409 creator A5011872468 @default.
- W2912996409 creator A5012456295 @default.
- W2912996409 creator A5017436855 @default.
- W2912996409 date "2019-01-28" @default.
- W2912996409 modified "2023-09-27" @default.
- W2912996409 title "The second maximal groups with respect to the sum of element orders" @default.
- W2912996409 cites W1980378955 @default.
- W2912996409 cites W2012860839 @default.
- W2912996409 cites W2093497308 @default.
- W2912996409 cites W2140025044 @default.
- W2912996409 cites W2158949661 @default.
- W2912996409 cites W2810953164 @default.
- W2912996409 cites W2962964556 @default.
- W2912996409 cites W3148349572 @default.
- W2912996409 hasPublicationYear "2019" @default.
- W2912996409 type Work @default.
- W2912996409 sameAs 2912996409 @default.
- W2912996409 citedByCount "1" @default.
- W2912996409 countsByYear W29129964092019 @default.
- W2912996409 crossrefType "posted-content" @default.
- W2912996409 hasAuthorship W2912996409A5011872468 @default.
- W2912996409 hasAuthorship W2912996409A5012456295 @default.
- W2912996409 hasAuthorship W2912996409A5017436855 @default.
- W2912996409 hasConcept C10138342 @default.
- W2912996409 hasConcept C114614502 @default.
- W2912996409 hasConcept C121332964 @default.
- W2912996409 hasConcept C136170076 @default.
- W2912996409 hasConcept C162324750 @default.
- W2912996409 hasConcept C182306322 @default.
- W2912996409 hasConcept C184992742 @default.
- W2912996409 hasConcept C20725272 @default.
- W2912996409 hasConcept C2781311116 @default.
- W2912996409 hasConcept C33923547 @default.
- W2912996409 hasConcept C62520636 @default.
- W2912996409 hasConceptScore W2912996409C10138342 @default.
- W2912996409 hasConceptScore W2912996409C114614502 @default.
- W2912996409 hasConceptScore W2912996409C121332964 @default.
- W2912996409 hasConceptScore W2912996409C136170076 @default.
- W2912996409 hasConceptScore W2912996409C162324750 @default.
- W2912996409 hasConceptScore W2912996409C182306322 @default.
- W2912996409 hasConceptScore W2912996409C184992742 @default.
- W2912996409 hasConceptScore W2912996409C20725272 @default.
- W2912996409 hasConceptScore W2912996409C2781311116 @default.
- W2912996409 hasConceptScore W2912996409C33923547 @default.
- W2912996409 hasConceptScore W2912996409C62520636 @default.
- W2912996409 hasLocation W29129964091 @default.
- W2912996409 hasOpenAccess W2912996409 @default.
- W2912996409 hasPrimaryLocation W29129964091 @default.
- W2912996409 hasRelatedWork W2026503104 @default.
- W2912996409 hasRelatedWork W2041081626 @default.
- W2912996409 hasRelatedWork W2072483316 @default.
- W2912996409 hasRelatedWork W2072736366 @default.
- W2912996409 hasRelatedWork W2263635792 @default.
- W2912996409 hasRelatedWork W2351420718 @default.
- W2912996409 hasRelatedWork W2393843578 @default.
- W2912996409 hasRelatedWork W2512589146 @default.
- W2912996409 hasRelatedWork W2542325467 @default.
- W2912996409 hasRelatedWork W2575213832 @default.
- W2912996409 hasRelatedWork W2735266215 @default.
- W2912996409 hasRelatedWork W2952396715 @default.
- W2912996409 hasRelatedWork W2953156712 @default.
- W2912996409 hasRelatedWork W2968588986 @default.
- W2912996409 hasRelatedWork W2972790884 @default.
- W2912996409 hasRelatedWork W2979476193 @default.
- W2912996409 hasRelatedWork W3073717275 @default.
- W2912996409 hasRelatedWork W3101693517 @default.
- W2912996409 hasRelatedWork W3128249154 @default.
- W2912996409 hasRelatedWork W3214197174 @default.
- W2912996409 isParatext "false" @default.
- W2912996409 isRetracted "false" @default.
- W2912996409 magId "2912996409" @default.
- W2912996409 workType "article" @default.