Equation 677 Database

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Magma 35a2460b0694…

magma 35a2460b0694
Size
321
Isomorphism class hash
35a2460b069491f3a8d3867467e12fbcd3f5e259524f1a50294479413462558a
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 22:45:10
Display reorder
300,161,122,52,131,141,50,162,132,123,142,163,124,51,133,140,55,160,130,125,144,158,53,128,126,145,54,159,129,127,143,152,47,137,120,147,153,48,138,121,148,154,49,139,119,146,46,155,136,116,150,44,156,134,117,151,45,157,135,118,149,305,307,311,306,262,261,249,263,260,250,253,254,252,255,257,256,251,258,259,248,273,274,272,275,264,246,266,265,267,247,269,270,268,271,285,240,286,284,287,277,241,278,276,279,281,242,282,280,283,243,297,298,296,299,244,288,290,289,291,245,293,294,292,295,320,319,317,318,58,3,20,32,166,21,56,33,4,164,57,2,22,34,165,23,61,35,6,169,59,24,36,7,167,25,60,37,5,168,64,26,38,225,224,62,27,39,0,170,63,28,40,1,171,29,67,41,237,236,30,65,42,229,228,31,66,43,233,232,302,301,314,316,214,174,109,100,185,107,212,98,172,186,213,173,108,99,184,105,217,103,177,188,215,106,101,175,189,104,216,102,176,187,220,115,95,180,191,218,113,96,178,192,219,114,97,179,190,111,223,94,183,194,112,221,92,181,195,110,222,93,182,193,312,303,308,309,207,198,17,72,82,18,205,73,196,80,206,197,19,71,81,16,210,68,201,85,208,14,69,199,83,15,209,70,200,84,227,8,78,226,88,211,9,79,202,86,204,10,77,203,87,11,239,74,238,91,12,231,75,230,89,13,235,76,234,90,315,310,304,313 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#8ecda3bf937b7c39d65eafcd0523fd56cf367f983a83102877b0cefff256addf, 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 22:45:11 · history