فهرست مطالب

  • Volume:6 Issue:3, 2017
  • تاریخ انتشار: 1396/06/01
  • تعداد عناوین: 5
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  • S. Mohsen Ghoraishi *, Marzieh Ahmadi Pages 1-4
    ýýIn this paper we determine all finite 2 -groups ofý ýclass 2 in which every automorphism of order 2 leaving the Frattini subgroup elementwise fixed is innerý.
    Keywords: ??Finite p -group of class 2 ?, ?non-inner automorphism?, ?Frattini subgroup
  • Naoya Yamaguchi * Pages 5-11
    For any given finite abelian groupý, ýwe give factorizations of the group determinant in the group algebra of any subgroupsý. ýThe factorizations is an extension of Dedekind's theoremý. ýThe extension leads to a generalization of Dedekind's theoremý.
    Keywords: ?Dedekind's theorem, group determinant, group algebra
  • Alan Camina, Rachel Camina * Pages 13-19
    A finite group G satisfies the on-prime power hypothesis for conjugacy class sizes if any two conjugacy class sizes m and n are either equal or have a common divisor a prime power. Taeri conjectured that an insoluble group satisfying this condition is isomorphic to StimesA where A is abelian and ScongPSL 2 (q) for qin4,8 . We confirm this conjecture.
    Keywords: conjugacy class sizes, finite groups, insoluble groups, bipartite graph
  • Simon Wacker * Pages 21-44
    ýWe introduce right amenabilityý, ýright FØlner netsý, ýand right paradoxical decompositions for left homogeneous spaces and prove the Tarski-FØlner theorem for left homogeneous spaces with finite stabilisersý. ýIt states that right amenabilityý, ýthe existence of right FØlner netsý, ýand the non-existence of right paradoxical decompositions are equivalentý.
    Keywords: ??left group actions?, ?right amenability?, ?right F?lner nets?, ?right paradoxical decompositions?, ?Tarski-F?lner theorem
  • Hossein Abdolzadeh *, Reza Sabzchi Pages 45-49
    ýýWe determine a new infinite sequence of finite 2 -groups with deficiency zeroý. ýThe groups have 2 generators and 2 relationsý, ýthey have coclass 3ý ýand they are not metacyclicý.
    Keywords: ?finite 2 -groups?, ?deficiency zero?, ?Schur multiplicator