Equation 677 Database

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Magma ee0691fa9c67…

magma ee0691fa9c67
Size
321
Isomorphism class hash
ee0691fa9c6739ae5ebf708b2555d9a333256f6af75a34a15a88ec6956c13db1
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 23:04:35
Display reorder
300,233,245,197,118,223,243,119,231,195,224,244,117,232,196,222,229,114,241,193,226,230,115,242,194,227,228,116,240,192,225,251,239,203,109,221,249,237,201,110,219,250,238,202,108,220,235,247,199,112,217,236,248,200,113,218,234,246,198,111,216,313,307,309,305,273,272,275,6,274,265,7,264,267,266,268,8,269,271,270,257,9,256,259,258,261,10,260,263,262,253,11,252,255,254,296,297,298,4,299,289,288,290,5,291,292,293,295,3,294,281,280,282,1,283,285,284,286,0,287,277,276,278,2,279,320,318,319,317,128,44,33,20,57,42,18,126,34,58,43,19,127,35,59,131,23,47,32,56,129,21,45,30,54,130,22,46,31,55,39,123,24,15,48,40,124,25,16,49,41,125,26,17,50,122,38,27,14,51,120,36,28,12,52,121,37,29,13,53,316,306,312,308,142,160,145,205,178,161,206,143,146,179,159,204,141,144,177,138,208,156,148,174,139,209,157,149,175,140,207,158,147,176,166,133,151,211,169,167,134,152,212,170,165,132,150,210,168,136,162,154,214,172,137,163,155,215,173,135,164,153,213,171,315,302,311,301,84,64,97,181,82,65,182,85,98,83,63,180,86,96,81,87,184,60,100,78,88,185,61,101,79,89,183,62,99,80,70,90,103,187,73,71,91,104,188,74,69,92,102,186,72,93,66,106,190,76,94,67,107,191,77,95,68,105,189,75,314,304,310,303 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#fbd23cd98406f165f23d6b41307d902a92b7e2e110ccd89116da4983a4804a48, 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 23:04:36 · history