Equation 677 Database

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Magma 77f79bf568a0…

magma 77f79bf568a0
Size
705
Isomorphism class hash
77f79bf568a027da500c813006977f2b36cbaf32b307241c9640791199197c56
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 16:28:31
Display reorder
660,452,24,449,450,453,472,25,470,469,473,423,26,433,432,434,27,512,510,509,513,28,532,530,529,533,29,492,490,489,493,575,569,30,570,576,595,589,31,590,596,555,549,32,550,556,629,635,33,630,636,649,655,34,650,656,609,615,35,610,616,691,685,694,690,451,139,441,444,440,471,140,464,461,460,422,138,429,426,425,142,511,504,501,500,143,531,524,520,521,141,491,484,481,480,572,561,137,564,560,592,581,135,584,580,552,541,136,544,540,620,632,133,624,621,640,652,134,644,641,601,612,132,604,600,701,697,703,699,385,181,373,398,337,386,182,400,374,338,384,180,396,372,336,184,388,404,376,340,185,389,406,377,341,183,387,402,375,339,391,379,187,411,343,392,380,188,413,344,390,378,186,409,342,382,394,190,417,346,383,395,191,419,347,381,393,189,415,345,677,681,672,679,361,117,301,90,399,362,118,91,302,401,360,119,92,300,397,116,364,93,304,405,114,365,94,305,407,115,363,95,303,403,367,307,108,88,410,368,308,109,89,412,366,306,110,87,408,310,370,111,84,416,311,371,112,85,418,309,369,113,86,414,664,671,682,675,442,153,456,457,458,462,154,477,476,478,427,155,437,436,438,152,502,516,517,518,150,522,537,538,539,151,482,496,497,498,562,571,144,573,574,582,591,145,593,594,542,551,146,553,554,631,622,147,633,634,651,642,148,653,654,611,602,149,613,614,687,686,688,695,459,53,445,446,454,479,51,466,465,474,439,52,431,430,435,49,519,506,505,514,50,536,526,525,534,48,499,486,485,494,579,565,59,566,577,599,585,57,586,597,559,545,58,546,557,625,639,55,626,637,645,659,56,646,657,605,619,54,606,617,698,702,696,704,443,44,447,455,448,463,42,475,467,468,428,43,424,420,421,47,503,515,507,508,45,523,535,527,528,46,483,495,487,488,563,567,39,578,568,583,587,40,598,588,543,547,41,558,548,627,623,38,638,628,647,643,36,658,648,607,603,37,618,608,693,700,689,692,349,4,313,201,169,350,5,202,314,170,348,3,203,312,168,1,352,200,316,172,0,353,198,317,173,2,351,199,315,171,355,319,10,192,175,356,320,11,193,176,354,318,9,194,174,322,358,6,195,178,323,359,7,196,179,321,357,8,197,177,665,684,661,673,325,17,74,102,67,326,15,103,72,68,324,16,104,73,66,13,328,105,77,70,14,329,106,75,71,12,327,107,76,69,331,80,23,100,65,332,78,21,101,63,330,79,22,99,64,83,334,19,96,61,81,335,20,97,62,82,333,18,98,60,667,676,674,666,283,131,265,289,262,284,129,290,266,263,282,130,288,264,261,127,286,292,268,258,128,287,293,269,259,126,285,291,267,260,281,271,122,295,253,279,272,120,296,254,280,270,121,294,252,274,277,125,298,256,275,278,123,299,257,273,276,124,297,255,662,663,678,683,233,160,221,245,209,231,161,243,219,207,232,159,244,220,208,156,229,241,217,205,157,230,242,218,206,158,228,240,216,204,239,227,166,251,215,237,225,167,249,213,238,226,165,250,214,223,235,162,247,211,224,236,163,248,212,222,234,164,246,210,669,680,670,668 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#33430dadf8546adceaddacfc75eeb6c00258f5413ce1926e16e948db7c79b4f3, M = {60} 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 2026-10-03 16:28:32 · history