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3 results

CHARACTERIZING n-ISOCLINIC CLASSES OF CROSSED MODULES

Structure and classification of infinite or finite groups
Special categories
Other generalizations of groups

HAJAR RAVANBOD, ALI REZA SALEMKAR, SAJEDEH TALEBTASH
Journal: Glasgow Mathematical Journal / Volume 61 / Issue 3 / September 2019
Published online by Cambridge University Press: 08 October 2018, pp. 637-656
Print publication: September 2019
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In this paper, we introduce the notion of the equivalence relation, called n-isoclinism, between crossed modules of groups, and give some basic properties of this notion. In particular, we obtain some criteria under which crossed modules are n-isoclinic. Also, we present the notion of n-stem crossed module and, under some conditions, determine them within an n-isoclinism class.

The commutator subgroup and Schur multiplier of a pair of finite p-groups

Structure and classification of infinite or finite groups

Ali Reza Salemkar, Mohammad Reza R. Moghaddam, Farshid Saeedi
Journal: Journal of the Australian Mathematical Society / Volume 81 / Issue 1 / August 2006
Published online by Cambridge University Press: 09 April 2009, pp. 1-10
Print publication: August 2006
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Let (M, G) be a pair of groups, in which M is a normal subgroup of G such that G/M and M/Z(M, G) are of orders pm and pn. respectively. In 1998, Ellis proved that the commutator subgroup [M, G] has order at most pn(n + 2 m−1)/2.
In the present paper by assuming /[M, G] = pn(n+2m−1)/2, we determine the pair (M, G). An upper bound is obtained for the Schur multiplier of the pair (M, G), which generalizes the work of Green (1956).

Some Properties on Isologism of Groups

Structure and classification of infinite or finite groups
Special aspects of infinite or finite groups

Mohammad Reza R. Moghaddam, Ali Reza Salemkar
Journal: Journal of the Australian Mathematical Society / Volume 68 / Issue 1 / February 2000
Published online by Cambridge University Press: 09 April 2009, pp. 1-9
Print publication: February 2000
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In this paper a necessary and sufficient condition will be given for groups to be ν-isologic, with respect to a given variety of groups ν. Its is also shown that every ν-isologism family of a group contains a ν-Hopfian group. Finally we show that if G is in the variety ν, then every ν-covering group of G is a Hopfian group.