Equation 677 Database

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Magma 0b28756f9848…

magma 0b28756f9848
Size
705
Isomorphism class hash
0b28756f984885824e6b54827794c29508eea8e265488a0b27ac3388e5735409
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 19:59:34
Display reorder
660,173,172,171,168,169,170,178,179,177,174,175,176,127,128,126,130,131,129,125,123,124,121,122,120,529,530,528,532,533,531,535,536,534,538,539,537,477,478,479,476,474,475,468,469,470,471,472,473,275,273,274,271,272,270,266,264,265,269,267,268,669,676,679,695,223,222,224,225,226,227,220,221,219,216,217,218,314,312,313,317,315,316,320,318,319,323,321,322,623,621,622,619,620,618,614,612,613,617,615,616,74,72,73,77,75,76,80,78,79,83,81,82,39,40,41,38,36,37,45,46,47,44,42,43,662,665,668,685,487,486,488,489,490,491,484,485,483,480,481,482,106,107,105,102,103,104,97,98,96,100,101,99,137,135,136,133,134,132,143,141,142,139,140,138,95,93,94,91,92,90,86,84,85,89,87,88,543,544,545,542,540,541,549,550,551,548,546,547,672,675,680,696,259,258,260,261,262,263,256,257,255,252,253,254,367,368,366,370,371,369,365,363,364,361,362,360,380,378,379,383,381,382,375,376,377,374,372,373,392,390,391,395,393,394,387,388,389,386,384,385,116,114,115,119,117,118,111,112,113,110,108,109,691,697,699,704,419,418,417,414,415,416,409,410,408,412,413,411,284,282,283,287,285,286,279,280,281,278,276,277,149,147,148,145,146,144,155,153,154,151,152,150,645,646,647,644,642,643,636,637,638,639,640,641,337,338,336,340,341,339,343,344,342,346,347,345,682,688,689,702,571,570,572,573,574,575,568,569,567,564,565,566,513,514,515,512,510,511,504,505,506,507,508,509,10,11,9,6,7,8,0,2,1,4,5,3,448,449,447,444,445,446,454,455,453,450,451,452,352,353,351,348,349,350,358,359,357,354,355,356,663,667,673,684,288,290,289,293,291,292,296,294,295,299,297,298,429,430,431,428,426,427,420,421,422,423,424,425,649,650,648,652,653,651,655,656,654,658,659,657,28,29,27,24,25,26,34,35,33,30,31,32,591,592,593,590,588,589,597,598,599,596,594,595,681,687,690,701,13,12,14,15,16,17,18,19,20,21,22,23,502,503,501,498,499,500,493,494,492,496,497,495,560,558,559,563,561,562,555,556,557,554,552,553,442,443,441,438,439,440,433,434,432,436,437,435,163,164,162,166,167,165,161,159,160,157,158,156,671,683,677,693,203,202,201,198,199,200,193,194,192,196,197,195,212,210,211,215,213,214,207,208,209,206,204,205,310,311,309,306,307,308,301,302,300,304,305,303,602,600,601,605,603,604,608,606,607,611,609,610,51,52,53,50,48,49,57,58,59,56,54,55,692,698,700,703,624,626,625,629,627,628,632,630,631,635,633,634,407,405,406,403,404,402,398,396,397,401,399,400,70,71,69,66,67,68,61,62,60,64,65,63,231,232,233,230,228,229,237,238,239,236,234,235,331,332,330,334,335,333,329,327,328,325,326,324,661,664,666,686,463,462,464,465,466,467,460,461,459,456,457,458,524,522,523,527,525,526,519,520,521,518,516,517,240,241,242,243,244,245,246,247,248,249,250,251,584,582,583,587,585,586,579,580,581,578,576,577,182,180,181,185,183,184,188,186,187,191,189,190,670,674,678,694 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#b841b444f6b6a6329111833cc0cf1c9cdaf118d6968b1c3e99c4136ce1352ec2, M = {61} in E, B = magma#abfd8e025ce71b705594dbbe1465dc1c7328d12d30e12d07906d7138f9d583bc. 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 19:59:35 · history