LEADER 08232nam 2200697 a 450 001 9910828489603321 005 20230725050853.0 010 $a1-283-40037-5 010 $a9786613400376 010 $a3-11-025448-4 024 7 $a10.1515/9783110254488 035 $a(CKB)2550000000041608 035 $a(EBL)737006 035 $a(OCoLC)743693632 035 $a(SSID)ssj0000530903 035 $a(PQKBManifestationID)11344131 035 $a(PQKBTitleCode)TC0000530903 035 $a(PQKBWorkID)10569930 035 $a(PQKB)11655033 035 $a(MiAaPQ)EBC737006 035 $a(DE-B1597)123541 035 $a(OCoLC)900775515 035 $a(OCoLC)978483275 035 $a(DE-B1597)9783110254488 035 $a(Au-PeEL)EBL737006 035 $a(CaPaEBR)ebr10485459 035 $a(CaONFJC)MIL340037 035 $a(EXLCZ)992550000000041608 100 $a20110809d2011 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aGroups of prime power order$hVolume 3$b[electronic resource] /$fYakov Berkovich, Zvonimir Janko 210 $aBerlin $cDe Gruyter$d2011 215 $a1 online resource (668 p.) 225 1 $aDe Gruyter expositions in mathematics,$x0938-6572 ;$v56 225 0 $aGroups of prime power order ;$vv. 3 300 $aIncludes indexes. 311 $a3-11-020717-6 327 $t Frontmatter -- $tContents -- $tList of definitions and notations -- $tPreface -- $tPrerequisites from Volumes 1 and 2 -- $t§93 Nonabelian 2-groups all of whose minimal nonabelian subgroups are metacyclic and have exponent 4 -- $t§94 Nonabelian 2-groups all of whose minimal nonabelian subgroups are nonmetacyclic and have exponent 4 -- $t§95 Nonabelian 2-groups of exponent 2e which have no minimal nonabelian subgroups of exponent 2e -- $t§96 Groups with at most two conjugate classes of nonnormal subgroups -- $t§97 p-groups in which some subgroups are generated by elements of order p -- $t§98 Nonabelian 2-groups all of whose minimal nonabelian subgroups are isomorphic to M2n+1, n 3 fixed -- $t§99 2-groups with sectional rank at most 4 -- $t§100 2-groups with exactly one maximal subgroup which is neither abelian nor minimal nonabelian -- $t§101 p-groups G with p > 2 and d(G) = 2 having exactly one maximal subgroup which is neither abelian nor minimal nonabelian -- $t§102 p-groups G with p > 2 and d(G) > 2 having exactly one maximal subgroup which is neither abelian nor minimal nonabelian -- $t§103 Some results of Jonah and Konvisser -- $t§104 Degrees of irreducible characters of p-groups associated with finite algebras -- $t§105 On some special p-groups -- $t§106 On maximal subgroups of two-generator 2-groups -- $t§107 Ranks of maximal subgroups of nonmetacyclic two-generator 2-groups -- $t§108 p-groups with few conjugate classes of minimal nonabelian subgroups -- $t§109 On p-groups with metacyclic maximal subgroup without cyclic subgroup of index p -- $t§110 Equilibrated p-groups -- $t§111 Characterization of abelian and minimal nonabelian groups -- $t§112 Non-Dedekindian p-groups all of whose nonnormal subgroups have the same order -- $t§113 The class of 2-groups in §70 is not bounded -- $t§114 Further counting theorems -- $t§115 Finite p-groups all of whose maximal subgroups except one are extraspecial -- $t§116 Groups covered by few proper subgroups -- $t§117 2-groups all of whose nonnormal subgroups are either cyclic or of maximal class -- $t§118 Review of characterizations of p-groups with various minimal nonabelian subgroups -- $t§119 Review of characterizations of p-groups of maximal class -- $t§120 Nonabelian 2-groups such that any two distinct minimal nonabelian subgroups have cyclic intersection -- $t§121 p-groups of breadth 2 -- $t§122 p-groups all of whose subgroups have normalizers of index at most p -- $t§123 Subgroups of finite groups generated by all elements in two shortest conjugacy classes -- $t§124 The number of subgroups of given order in a metacyclic p-group -- $t§125 p-groups G containing a maximal subgroup H all of whose subgroups are G-invariant -- $t§126 The existence of p-groups G1 G such that Aut(G1) Aut(G) -- $t§127 On 2-groups containing a maximal elementary abelian subgroup of order 4 -- $t§128 The commutator subgroup of p-groups with the subgroup breadth 1 -- $t§129 On two-generator 2-groups with exactly one maximal subgroup which is not two-generator -- $t§130 Soft subgroups of p-groups -- $t§131 p-groups with a 2-uniserial subgroup of order p -- $t§132 On centralizers of elements in p-groups -- $t§133 Class and breadth of a p-group -- $t§134 On p-groups with maximal elementary abelian subgroup of order p2 -- $t§135 Finite p-groups generated by certain minimal nonabelian subgroups -- $t§136 p-groups in which certain proper nonabelian subgroups are two-generator -- $t§137 p-groups all of whose proper subgroups have its derived subgroup of order at most p -- $t§138 p-groups all of whose nonnormal subgroups have the smallest possible normalizer -- $t§139 p-groups with a noncyclic commutator group all of whose proper subgroups have a cyclic commutator group -- $t§140 Power automorphisms and the norm of a p-group -- $t§141 Nonabelian p-groups having exactly one maximal subgroup with a noncyclic center -- $t§142 Nonabelian p-groups all of whose nonabelian maximal subgroups are either metacyclic or minimal nonabelian -- $t§143 Alternate proof of the Reinhold Baer theorem on 2-groups with nonabelian norm -- $t§144 p-groups with small normal closures of all cyclic subgroups -- $tAppendix 27 Wreathed 2-groups -- $tAppendix 28 Nilpotent subgroups -- $tAppendix 29 Intersections of subgroups -- $tAppendix 30 Thompson's lemmas -- $tAppendix 31 Nilpotent p'-subgroups of class 2 in GL(n, p) -- $tAppendix 32 On abelian subgroups of given exponent and small index -- $tAppendix 33 On Hadamard 2-groups -- $tAppendix 34 Isaacs-Passman's theorem on character degrees -- $tAppendix 35 Groups of Frattini class 2 -- $tAppendix 36 Hurwitz' theorem on the composition of quadratic forms -- $tAppendix 37 On generalized Dedekindian groups -- $tAppendix 38 Some results of Blackburn and Macdonald -- $tAppendix 39 Some consequences of Frobenius' normal p-complement theorem -- $tAppendix 40 Varia -- $tAppendix 41 Nonabelian 2-groups all of whose minimal nonabelian subgroups have cyclic centralizers -- $tAppendix 42 On lattice isomorphisms of p-groups of maximal class -- $tAppendix 43 Alternate proofs of two classical theorems on solvable groups and some related results -- $tAppendix 44 Some of Freiman's results on finite subsets of groups with small doubling -- $tResearch problems and themes III -- $tAuthor index -- $tSubject index 330 $aThis is the third volume of a comprehensive and elementary treatment of finite p-group theory. Topics covered in this volume: impact of minimal nonabelian subgroups on the structure of p-groups, classification of groups all of whose nonnormal subgroups have the same order, degrees of irreducible characters of p-groups associated with finite algebras, groups covered by few proper subgroups, p-groups of element breadth 2 and subgroup breadth 1, exact number of subgroups of given order in a metacyclic p-group, soft subgroups, p-groups with a maximal elementary abelian subgroup of order p2, p-groups generated by certain minimal nonabelian subgroups, p-groups in which certain nonabelian subgroups are 2-generator. The book contains many dozens of original exercises (with difficult exercises being solved) and a list of about 900 research problems and themes. 410 0$aDe Gruyter expositions in mathematics ;$v56. 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 I?A. G.$f1938-$01679268 701 $aJanko$b Zvonimir$f1932-$01142671 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910828489603321 996 $aGroups of prime power order$94047376 997 $aUNINA