Equation 677 Database

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Magma d6d3ed5a1705…

magma d6d3ed5a1705
Size
705
Isomorphism class hash
d6d3ed5a1705cd4118ff7ef5b46788368695784e57cf284a0770043e8645ef9d
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 19:18:11
Display reorder
660,12,490,109,450,396,10,491,110,451,397,11,489,111,449,395,8,486,108,446,392,9,487,106,447,393,7,488,107,448,394,115,481,3,441,387,116,482,0,442,388,117,480,2,440,386,484,114,6,444,390,485,112,4,445,391,483,113,5,443,389,680,675,674,683,254,73,466,154,327,255,74,467,152,328,256,75,465,153,326,253,72,462,150,323,251,70,463,151,324,252,71,464,149,325,457,79,245,160,318,458,80,246,158,319,456,81,247,159,317,78,460,248,156,321,76,461,249,157,322,77,459,250,155,320,672,663,666,664,87,351,478,526,550,85,352,479,527,551,86,350,477,525,549,83,347,474,522,546,84,348,475,523,547,82,349,476,524,548,469,342,93,517,541,470,343,91,518,542,468,341,92,516,540,345,472,89,520,544,346,473,90,521,545,344,471,88,519,543,686,687,681,673,166,647,650,646,644,164,655,658,654,652,165,639,642,638,637,162,615,618,614,613,163,623,626,622,621,161,631,634,630,629,565,243,172,239,235,566,241,170,240,236,564,242,171,238,234,596,599,168,601,600,608,610,169,607,606,244,567,167,237,233,703,698,700,704,41,363,339,275,408,42,364,340,276,409,40,362,338,277,407,44,359,335,278,404,45,360,336,279,405,43,361,337,280,406,330,354,39,273,399,331,355,37,274,400,329,353,38,272,398,357,333,35,269,402,358,334,36,270,403,356,332,34,271,401,689,692,690,691,50,562,303,283,538,51,563,304,281,539,49,561,302,282,537,46,558,299,286,534,47,559,300,284,535,48,560,301,285,536,294,553,56,289,529,295,554,57,287,530,293,552,55,288,528,556,297,52,292,532,557,298,53,290,533,555,296,54,291,531,667,669,662,670,121,212,311,198,193,122,213,312,199,191,123,214,313,197,192,120,211,314,201,196,118,209,315,202,194,119,210,316,200,195,309,218,127,204,188,310,219,128,205,189,308,220,129,203,190,217,305,126,207,187,215,306,124,208,185,216,307,125,206,186,693,695,696,694,94,514,437,502,594,95,515,439,503,595,96,513,435,501,593,97,510,31,498,590,98,511,32,499,591,99,512,33,500,592,26,505,100,493,585,27,506,101,494,586,25,504,102,492,584,508,29,103,496,588,509,30,104,497,589,507,28,105,495,587,684,688,678,685,230,651,645,648,649,231,659,653,656,657,232,643,636,640,641,229,619,612,616,617,227,627,620,624,625,228,635,628,632,633,134,570,221,132,453,135,568,222,133,454,136,569,223,131,452,603,602,224,597,598,611,605,225,604,609,571,1,226,130,455,699,697,702,701,66,432,262,146,582,64,433,260,147,583,65,431,261,148,581,69,428,258,145,578,67,429,259,143,579,68,430,257,144,580,268,423,61,137,573,266,424,62,138,574,267,422,63,139,572,426,264,60,140,576,427,265,58,141,577,425,263,59,142,575,668,671,661,665,19,436,420,367,183,20,438,421,365,184,21,434,419,366,182,22,385,416,370,179,23,383,417,368,180,24,384,418,369,181,411,377,17,373,174,412,378,18,371,175,410,379,16,372,173,380,414,13,376,177,381,415,14,374,178,382,413,15,375,176,682,676,677,679 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#9a5b705888933f32bf6ccbec2fa43e8b7ad7ed280396865bc2fba9cb62c49c59, M = {60} 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 19:18:12 · history