Equation 677 Database

← all  ·  ← by size  ·  ← size 720

Magma 266b54c14326…

magma 266b54c14326
Size
720
Isomorphism class hash
266b54c14326a6ebe6e864b207c7aae3fc536d076b2b92808b7d29ceb4c58459
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 719) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-06 09:14:56
Display reorder
61,62,63,64,65,66,67,68,69,70,71,72,73,74,60,719,50,33,26,51,27,34,52,28,35,53,29,36,54,15,37,55,16,38,17,39,56,57,18,40,58,19,41,59,20,42,45,21,43,46,22,44,47,23,30,48,24,31,49,25,32,8,1,0,2,3,4,5,6,7,10,11,12,13,14,9,718,716,717,715,674,672,671,673,452,464,659,453,465,660,454,466,661,455,467,662,456,468,457,469,663,664,458,470,665,459,471,666,460,472,667,461,473,668,462,474,669,463,475,670,451,476,658,450,477,435,442,443,444,445,446,447,448,449,437,438,439,440,441,436,703,705,704,706,277,259,308,278,309,260,279,310,261,280,311,262,281,312,263,282,313,264,314,265,283,284,300,266,270,301,267,271,302,268,272,303,269,273,304,255,274,305,256,275,306,257,276,307,258,289,296,297,298,299,285,286,287,288,291,292,293,294,295,290,690,688,689,687,179,163,142,165,143,164,166,144,150,167,145,151,168,146,152,169,147,153,148,154,170,171,149,155,172,135,156,173,136,157,174,137,158,175,138,159,176,139,160,177,140,161,178,141,162,189,181,182,183,184,185,186,187,188,191,192,193,194,180,190,697,695,698,696,430,414,393,431,394,415,432,395,416,433,396,417,434,397,418,420,398,419,399,405,421,422,400,406,423,401,407,424,402,408,425,403,409,426,404,410,427,390,411,428,391,412,429,392,413,375,382,383,384,385,386,387,388,389,377,378,379,380,381,376,710,709,707,708,94,77,124,95,125,78,96,126,79,97,127,80,98,128,81,99,129,82,130,83,100,101,131,84,102,132,85,103,133,86,104,134,87,90,120,88,91,121,89,92,122,75,93,123,76,105,112,113,114,115,116,117,118,119,107,108,109,110,111,106,712,713,711,714,603,654,632,604,633,655,605,634,656,606,635,657,607,636,643,608,637,644,638,645,609,610,639,646,611,640,647,612,641,648,598,642,649,599,628,650,600,629,651,601,630,652,602,631,653,613,620,621,622,623,624,625,626,627,615,616,617,618,619,614,701,702,700,699,320,372,351,321,352,373,322,353,374,323,354,360,324,355,361,325,356,362,357,363,326,327,358,364,328,359,365,329,345,366,315,346,367,316,347,368,317,348,369,318,349,370,319,350,371,332,339,340,341,342,343,344,330,331,334,335,336,337,338,333,677,675,678,676,253,237,216,254,217,238,240,218,239,241,219,225,242,220,226,243,221,227,222,228,244,245,223,229,246,224,230,247,210,231,248,211,232,249,212,233,250,213,234,251,214,235,252,215,236,199,206,207,208,209,195,196,197,198,201,202,203,204,205,200,693,691,692,694,479,530,508,480,509,531,481,510,532,482,511,533,483,512,534,484,513,535,514,536,485,486,515,537,487,516,523,488,517,524,489,518,525,490,519,526,491,520,527,492,521,528,478,522,529,505,497,498,499,500,501,502,503,504,507,493,494,495,496,506,679,682,680,681,562,546,589,563,590,547,564,591,548,565,592,549,566,593,550,567,594,551,595,552,553,554,596,538,555,597,539,556,583,540,557,584,541,558,585,542,559,586,543,560,587,544,561,588,545,572,579,580,581,582,568,569,570,571,574,575,576,577,578,573,683,684,686,685 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 720 = 16 + 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#7fd9b57d9d47f149dcae21b99bbb486e9ed16acb343863fc90869d5061310077, M = {0, 4, 8, 12, 16, 20, 26, 28, 32, 36, 40, 44, 48, 52, 57, 77} in E, B = magma#9878faa9b07066f62fc077f7c99df5b1f6f079c61c0cd7e7f5bbdb9bc181adbc. 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 2026-10-06 09:14:57 · history