Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma d47873f0fb39…

magma d47873f0fb39
Size
705
Isomorphism class hash
d47873f0fb39431397a842d1344a47181583e3735fe9ee71beb298d878653523
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 704) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-03 20:10:36
Display reorder
660,495,423,130,214,399,128,496,212,400,424,129,425,497,213,401,422,133,494,217,398,420,131,492,215,396,421,132,493,216,397,220,414,486,136,390,218,415,487,134,391,219,416,488,135,392,417,223,489,139,393,418,221,490,137,394,138,419,222,491,395,663,667,672,664,565,483,177,74,146,178,566,75,147,484,176,485,567,76,148,482,180,564,77,149,480,181,562,78,150,481,179,563,79,151,72,474,556,183,144,73,475,557,184,145,71,476,558,182,143,477,68,559,186,140,478,69,560,187,141,185,479,70,561,142,690,688,685,686,387,553,246,311,447,247,388,312,448,554,245,555,389,313,449,552,242,386,310,446,550,243,384,308,444,551,244,385,309,445,317,544,378,237,438,318,545,379,238,439,319,546,380,236,440,547,316,381,240,441,548,314,382,241,442,239,549,315,383,443,665,661,669,670,82,531,257,157,459,258,80,155,460,532,259,533,81,156,461,530,256,85,153,458,528,254,83,154,456,529,255,84,152,457,163,522,88,248,450,161,523,86,249,451,162,524,87,250,452,525,159,91,251,453,526,160,89,252,454,253,527,158,90,455,675,677,679,678,577,519,39,175,345,40,578,173,346,520,38,521,579,174,347,518,42,576,171,344,516,43,574,172,342,517,41,575,170,343,166,510,568,37,351,164,511,569,35,352,165,512,570,36,353,513,169,571,33,350,514,167,572,34,348,32,515,168,573,349,666,671,662,668,228,411,61,507,611,59,229,508,612,412,60,413,227,509,613,410,57,224,506,610,408,58,225,504,608,409,56,226,505,609,498,402,234,67,602,499,403,235,65,603,500,404,233,66,604,405,501,230,63,605,406,502,231,64,606,62,407,503,232,607,697,693,696,695,601,326,331,28,647,332,655,654,652,653,330,659,657,656,658,327,334,600,29,644,328,335,598,30,645,329,333,599,31,646,26,324,592,337,639,27,325,593,338,640,25,323,594,336,638,320,22,595,340,642,321,23,596,341,643,339,322,24,597,641,702,703,701,704,1,375,361,623,540,362,648,624,649,376,360,377,651,625,650,374,364,2,622,541,372,365,3,620,542,373,363,0,621,543,614,366,5,359,538,615,367,6,357,539,616,368,4,358,537,369,617,8,355,534,370,618,9,356,535,354,371,619,7,536,700,699,698,694,471,116,200,110,51,201,472,111,52,117,202,118,473,112,50,119,203,470,113,54,120,204,468,114,55,121,205,469,115,53,108,122,462,206,49,109,123,463,207,47,107,124,464,208,48,125,104,465,209,45,126,105,466,210,46,211,127,106,467,44,681,676,684,673,296,435,14,589,635,15,297,590,636,436,13,437,298,591,637,434,10,299,588,634,432,11,300,586,632,433,12,301,587,633,580,426,302,20,626,581,427,303,21,627,582,428,304,19,628,429,583,305,16,629,430,584,306,17,630,18,431,585,307,631,683,682,680,674,266,99,196,294,274,194,267,295,272,100,195,98,268,293,273,102,199,269,290,277,103,197,270,291,275,101,198,271,292,276,285,97,264,191,280,286,95,265,192,278,284,96,263,193,279,93,288,260,190,283,94,289,261,188,281,189,92,287,262,282,687,689,691,692 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 705 = 1 + 11*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, 11, B) with E = magma#bc84586c53073a7227d3f1cff463f9e10a3c0feadba644a539b68478442af133, M = {60} in E, B = magma#ca58a4a9ddeee171fc40b5c556a5095e4a2c63eee13557dcdf190986f06d14c3. 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(11, 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: 45.

last edited by qawbecrdtey at 2026-10-03 20:10:37 · history