LEADER 06969nam 2200733Ia 450 001 9910782769603321 005 20200520144314.0 010 $a1-281-99348-4 010 $a9786611993481 010 $a3-11-916239-6 010 $a3-11-020823-7 024 7 $a10.1515/9783110208238 035 $a(CKB)1000000000698065 035 $a(EBL)429232 035 $a(OCoLC)808801274 035 $a(SSID)ssj0000165946 035 $a(PQKBManifestationID)11164402 035 $a(PQKBTitleCode)TC0000165946 035 $a(PQKBWorkID)10147207 035 $a(PQKB)10094424 035 $a(MiAaPQ)EBC429232 035 $a(DE-B1597)34859 035 $a(OCoLC)931571208 035 $a(OCoLC)953314427 035 $a(DE-B1597)9783110208238 035 $a(Au-PeEL)EBL429232 035 $a(CaPaEBR)ebr10275912 035 $a(CaONFJC)MIL199348 035 $z(PPN)17552386X 035 $a(PPN)140884521 035 $a(EXLCZ)991000000000698065 100 $a20081001d2008 uy 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt 182 $cc 183 $acr 200 10$aGroups of prime power order$hVolume 2$b[electronic resource] /$fby Yakov Berkovich and Zvonimir Janko 210 $aBerlin ;$aNew York $cW. de Gruyter$dc2008 215 $a1 online resource (612 p.) 225 1 $aDe Gruyter expositions in mathematics,$x0938-6572 ;$v47 300 $aDescription based upon print version of record. 311 $a3-11-020419-3 320 $aIncludes bibliographical references and indexes. 327 $t Frontmatter -- $tContents -- $tList of definitions and notations -- $tPreface -- $t§46. Degrees of irreducible characters of Suzuki p-groups -- $t§47. On the number of metacyclic epimorphic images of finite p-groups -- $t§48. On 2-groups with small centralizer of an involution, I -- $t§49. On 2-groups with small centralizer of an involution, II -- $t§50. Janko's theorem on 2-groups without normal elementary abelian subgroups of order 8 -- $t§51. 2-groups with self centralizing subgroup isomorphic to E8 -- $t§52. 2-groups with 2-subgroup of small order -- $t§53. 2-groups G with c2(G) = 4 -- $t§54. 2-groups G with cn(G) = 4, n > 2 -- $t§55. 2-groups G with small subgroup (x ? G | o(x) = 2") -- $t§56. Theorem of Ward on quaternion-free 2-groups -- $t§57. Nonabelian 2-groups all of whose minimal nonabelian subgroups are isomorphic and have exponent 4 -- $t§58. Non-Dedekindian p-groups all of whose nonnormal subgroups of the same order are conjugate -- $t§59. p-groups with few nonnormal subgroups -- $t§60. The structure of the Burnside group of order 212 -- $t§61. Groups of exponent 4 generated by three involutions -- $t§62. Groups with large normal closures of nonnormal cyclic subgroups -- $t§63. Groups all of whose cyclic subgroups of composite orders are normal -- $t§64. p-groups generated by elements of given order -- $t§65. A2-groups -- $t§66. A new proof of Blackburn's theorem on minimal nonmetacyclic 2-groups -- $t§67. Determination of U2-groups -- $t§68. Characterization of groups of prime exponent -- $t§69. Elementary proofs of some Blackburn's theorems -- $t§70. Non-2-generator p-groups all of whose maximal subgroups are 2-generator -- $t§71. Determination of A2-groups -- $t§72. An-groups, n > 2 -- $t§73. Classification of modular p-groups -- $t§74. p-groups with a cyclic subgroup of index p2 -- $t§75. Elements of order ? in p-groups -- $t§76. p-groups with few A1-subgroups -- $t§77. 2-groups with a self-centralizing abelian subgroup of type (4, 2) -- $t§78. Minimal nonmodular p-groups -- $t§79. Nonmodular quaternion-free 2-groups -- $t§80. Minimal non-quaternion-free 2-groups -- $t§81. Maximal abelian subgroups in 2-groups -- $t§82. A classification of 2-groups with exactly three involutions -- $t§83. p-groups G with ?2(G) or ?2*(G) extraspecial -- $t§84. 2-groups whose nonmetacyclic subgroups are generated by involutions -- $t§85. 2-groups with a nonabelian Frattini subgroup of order 16 -- $t§86. p-groups G with metacyclic ?2*(G) -- $t§87. 2-groups with exactly one nonmetacyclic maximal subgroup -- $t§88. Hall chains in normal subgroups of p-groups -- $t§89. 2-groups with exactly six cyclic subgroups of order 4 -- $t§90. Nonabelian 2-groups all of whose minimal nonabelian subgroups are of order 8 -- $t§91. Maximal abelian subgroups of p-groups -- $t§92. On minimal nonabelian subgroups of p-groups -- $tAppendix 16. Some central products -- $tAppendix 17. Alternate proofs of characterization theorems of Miller and Janko on 2-groups, and some related results -- $tAppendix 18. Replacement theorems -- $tAppendix 19. New proof of Ward's theorem on quaternion-free 2-groups -- $tAppendix 20. Some remarks on automorphisms -- $tAppendix 21. Isaacs' examples -- $tAppendix 22. Minimal nonnilpotent groups -- $tAppendix 23. Groups all of whose noncentral conjugacy classes have the same size -- $tAppendix 24. On modular 2-groups -- $tAppendix 25. Schreier's inequality for p-groups -- $tAppendix 26. p-groups all of whose nonabelian maximal subgroups are either absolutely regular or of maximal class -- $tResearch problems and themes II -- $t Backmatter 330 $aThis is the second of three volumes devoted to elementary finite p-group theory. Similar to the first volume, hundreds of important results are analyzed and, in many cases, simplified. Important topics presented in this monograph include: (a) classification of p-groups all of whose cyclic subgroups of composite orders are normal, (b) classification of 2-groups with exactly three involutions, (c) two proofs of Ward's theorem on quaternion-free groups, (d) 2-groups with small centralizers of an involution, (e) classification of 2-groups with exactly four cyclic subgroups of order 2n ? 2, (f) two new proofs of Blackburn's theorem on minimal nonmetacyclic groups, (g) classification of p-groups all of whose subgroups of index p2 are abelian, (h) classification of 2-groups all of whose minimal nonabelian subgroups have order 8, (i) p-groups with cyclic subgroups of index p2 are classified. This volume contains hundreds of original exercises (with all difficult exercises being solved) and an extended list of about 700 open problems. The book is based on Volume 1, and it is suitable for researchers and graduate students of mathematics with a modest background on algebra. 410 0$aGruyter expositions in mathematics ;$v47. 606 $aFinite groups 606 $aGroup theory 610 $aGroup Theory. 610 $aOrder. 610 $aPrimes. 615 0$aFinite groups. 615 0$aGroup theory. 676 $a512.23 700 $aBerkovich$b Yakov$0472302 701 $aJanko$b Zvonimir$01142671 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910782769603321 996 $aGroups of prime power order$93803999 997 $aUNINA