Equation 677 Database

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Magma 5e880264a9fb…

magma 5e880264a9fb
Size
321
Isomorphism class hash
5e880264a9fb44228cd61b7f916200f954dcef8fb4f866978b713f85d733af12
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 320) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 22:27:50
Display reorder
300,30,48,229,228,63,31,232,49,233,64,50,236,32,237,65,224,33,51,225,62,216,34,52,217,60,220,35,53,221,61,54,72,75,28,69,55,73,76,29,70,56,74,77,27,71,204,57,205,24,68,209,58,208,25,66,213,59,212,26,67,306,301,315,316,242,290,289,291,288,240,294,295,293,292,299,298,241,297,296,287,245,286,285,284,279,243,278,277,276,283,244,282,281,280,254,255,253,248,252,258,259,257,246,256,262,263,261,247,260,267,266,264,251,265,271,270,268,249,269,275,274,272,250,273,319,318,320,317,78,159,201,186,166,79,187,160,202,167,161,188,80,203,165,185,81,162,200,169,183,82,163,198,170,184,83,164,199,168,157,177,192,84,172,158,178,193,85,173,156,179,194,86,171,180,153,195,87,175,181,154,196,88,176,182,155,197,89,174,302,304,305,311,147,40,230,11,231,148,9,41,234,235,39,10,149,238,239,7,150,36,226,227,8,151,37,218,219,6,152,38,222,223,46,2,91,145,189,47,1,92,146,190,45,0,90,144,191,5,42,207,141,206,3,43,210,142,211,4,44,214,143,215,308,313,309,314,16,94,126,137,116,17,135,95,127,114,93,136,15,128,115,140,12,97,125,112,138,13,98,123,113,139,14,96,124,111,100,132,117,22,107,101,133,118,23,105,99,134,119,21,106,131,103,120,18,110,129,104,121,19,108,130,102,122,20,109,310,307,312,303 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 321 = 1 + 5*64, from a common submagma at infinity. C(E, M, k, B) adjoins a submagma M (m elements) of a model E to every group of a transversal design TD(k, g), g = |E| - m, so that every enlarged group is a copy of E and all of them share M; every block carries B, a model of order k in which x*x = x. Two elements of M multiply in M; an element of M or of group i with one of group i, in group i's copy of E; elements of different groups, in their block. It satisfies Equation 677 whenever E and B do. This magma is C(E, M, 5, B) with E = magma#3a4a415766bc24344b8990a318a493c1fb50830922fededbbeb9b2ef7d49358b, M = {60} in E, B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5. Labels: 0..m-1 are M, in increasing order of their labels in E; m + g*i + c (i < k, c < g) is point c of group i, which plays the c-th element of E outside M, in increasing order. A block's point in group i plays element i of B. TD(5, 64): MacNeish's product over GF(64); GF(64) = F_2[x]/(x^6 + x + 1); GF(p^r) = F_p[x]/(f) labels c_0 + c_1 x + ... as c_0 + c_1 p + ..., and point c of a group is the c-th element of the product in lexicographic order. Block (a, b), a and b in the product, meets group i in the point whose coordinate in each field is a + s_i b, s_i the element of that field labelled i, or b when the field has exactly i elements. Equation 255: satisfied. Idempotent elements: 21.

last edited by qawbecrdtey at 2026-10-01 22:27:51 · history