๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Prime power groups which are cyclic extensions of elementary abelian groups

โœ Scribed by Gerhard Pazderski

Publisher
John Wiley and Sons
Year
1980
Tongue
English
Weight
562 KB
Volume
97
Category
Article
ISSN
0025-584X

No coin nor oath required. For personal study only.

โœฆ Synopsis

lGl=p", where n=n,+n,+. , . + n r 2 ) like 1) with apnn=b,, instead of apnn=l. Proof. Let G be a group of order p" with an elementary abelian normal subgroup B for which GIB is cyclic of order p"". Further let aB be a generating element of GIB. Then upnn B. The group (a) suffers from B a representation over G P ( p ) when B is in a natural manner considered to be a representation module for G'. Let (apk) be the kernel of this representation. Because of apnOC B we have CIP~'" E (cL~'"). Now we transform the representation such that CL is mapped into a matrix with JORDAN normal form, i.e. into a matrix shaped like where with a certain degree ni. A corresponding basis of B may be constituted by the elements b, (i= 1 , . . . , r ; j = 1, . . . , ni) under lexicographical order. Obviously BI= (bij j j= 1, . . . , ni) is a normal subgroup of G which affords the representation a+ai and we have

๐Ÿ“œ SIMILAR VOLUMES

Connected Cayley graphs of semi-direct p
Connected Cayley graphs of semi-direct products of cyclic groups of prime order by abelian groups are hamiltonian
โœ Erich Durnberger ๐Ÿ“‚ Article ๐Ÿ“… 1983 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 705 KB

In this paper it is shown that every connected Cayley graph of a semt-direct product of a cyclic group of prime order by an abelian group is hamiltonian. In particular, every connected Cayley graph of a group G is hamiltonian provided that G is of order greater than 2 and it contains a normal cyclic

A Classification of DCI(CI)-Subsets for
A Classification of DCI(CI)-Subsets for Cyclic Group of Odd Prime Power Order
โœ Qiongxiang Huang; Jixiang Meng ๐Ÿ“‚ Article ๐Ÿ“… 2000 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 175 KB

Let Z n be a cyclic group of order n and ) implies that S and T are conjugate in Aut(Z n ), the automorphism group of Z n . In this paper, we give a complete classification for DCI-subsets of Z n in the case of n= p a , where p is an odd prime.