Rogério, José Robério A note on maximal coverings of groups. (English) Zbl 1304.20043 Commun. Algebra 42, No. 10, 4498-4508 (2014). Summary: Let \(\lambda(G)\) be the maximum number of subgroups in an irredundant covering of the finite group \(G\). In this note we investigate the basic properties of \(\lambda(G)\), classify the groups for which \(\lambda(G)=3\), \(4\), \(5\) and also classify the nilpotent groups that admit only one-sized coverings. Cited in 1 ReviewCited in 5 Documents MSC: 20D60 Arithmetic and combinatorial problems involving abstract finite groups 20D30 Series and lattices of subgroups 20D15 Finite nilpotent groups, \(p\)-groups 20E28 Maximal subgroups Keywords:finite groups; irredundant coverings; maximal coverings; unions of subgroups; covers of groups by subgroups; finite nilpotent groups PDFBibTeX XMLCite \textit{J. R. Rogério}, Commun. Algebra 42, No. 10, 4498--4508 (2014; Zbl 1304.20043) Full Text: DOI References: [1] DOI: 10.1081/AGB-200066157 · Zbl 1117.20016 · doi:10.1081/AGB-200066157 [2] DOI: 10.1016/j.jpaa.2006.05.021 · Zbl 1117.20017 · doi:10.1016/j.jpaa.2006.05.021 [3] Abdollahi A., Publ. Math. Debrecen 72 (1) pp 167– (2008) [4] DOI: 10.1007/s100110300013 · Zbl 1030.20013 · doi:10.1007/s100110300013 [5] DOI: 10.1017/S0004972700034109 · Zbl 0883.20014 · doi:10.1017/S0004972700034109 [6] DOI: 10.1017/S1446788700002809 · Zbl 0997.20034 · doi:10.1017/S1446788700002809 [7] Cohn J. H. E., Math. Scand. 75 pp 44– (1994) · Zbl 0833.20028 · doi:10.7146/math.scand.a-12501 [8] Greco D., Rend. Sem. Mat. Univ. Padova 22 pp 313– (1953) [9] Greco D., Rend. Accad. Sci. Fis. Math. Napoli 23 (4) pp 49– (1956) [10] Humphreys J. F., A Course in Group Theory (1996) · Zbl 0843.20001 [11] DOI: 10.1007/978-3-642-64981-3 · Zbl 0217.07201 · doi:10.1007/978-3-642-64981-3 [12] DOI: 10.1142/S1005386705000659 · Zbl 1082.20009 · doi:10.1142/S1005386705000659 [13] DOI: 10.1016/j.jcta.2004.10.003 · Zbl 1066.20004 · doi:10.1016/j.jcta.2004.10.003 [14] DOI: 10.1007/978-1-4684-0128-8 · doi:10.1007/978-1-4684-0128-8 [15] DOI: 10.1080/00927878708823438 · doi:10.1080/00927878708823438 [16] Tomkinson M. J., Math. Scand. 81 pp 189– (1999) [17] Scorza G., Boll. Un. Mat. Ital. 5 pp 216– (1926) [18] Zhang J., Serdica Math. J. 32 (2) pp 259– (2006) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.