Equation 677 Database

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Magma 574d66bdcb35…

magma 574d66bdcb35
Size
705
Isomorphism class hash
574d66bdcb35164bcf21c809ab78cb84e3c7def35813234341b606fe51109e8c
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 20:35:04
Display reorder
660,487,343,2,316,304,1,485,314,302,341,0,342,486,315,303,339,5,483,319,307,340,3,484,317,305,338,4,482,318,306,493,8,349,322,310,491,6,347,320,308,492,7,348,321,309,11,489,345,325,313,9,490,346,323,311,324,10,488,344,312,663,672,665,662,206,157,568,463,523,566,207,461,521,158,567,156,208,462,522,153,564,209,459,519,154,565,210,460,520,155,563,211,458,518,212,574,148,469,529,213,572,149,467,527,214,573,147,468,528,570,215,151,465,525,571,216,152,466,526,464,569,217,150,524,688,689,692,691,580,271,355,547,451,353,578,545,449,269,354,270,579,546,450,267,351,576,543,447,268,352,577,544,448,266,350,575,542,446,586,361,277,553,457,584,359,275,551,455,585,360,276,552,456,357,582,273,549,453,358,583,274,550,454,548,356,581,272,452,667,664,669,661,161,228,592,439,15,590,159,437,16,229,591,227,160,438,17,224,588,164,435,14,225,589,162,436,12,226,587,163,434,13,613,598,219,445,614,165,596,220,443,169,611,597,218,444,612,594,168,222,441,20,595,166,223,442,18,440,593,167,221,19,676,680,681,678,511,109,629,236,171,627,509,237,172,110,628,108,510,238,170,105,625,507,239,174,106,626,508,240,175,107,624,506,241,173,517,635,100,234,177,515,633,101,235,178,516,634,99,233,176,631,513,103,230,180,632,514,104,231,181,232,630,512,102,179,668,670,666,671,253,37,331,367,265,329,251,365,263,38,330,36,252,366,264,40,327,249,363,261,41,328,250,364,262,39,326,248,362,260,244,337,35,373,256,242,335,33,371,254,243,336,34,372,255,333,247,31,369,259,334,245,32,370,257,368,332,246,30,258,700,699,693,694,558,93,28,74,620,29,559,72,618,94,27,95,557,73,619,96,24,554,70,616,97,25,555,71,617,98,26,556,69,615,656,658,91,657,659,651,649,92,648,650,652,654,90,653,655,22,560,87,68,622,23,561,88,66,623,67,21,562,89,621,702,704,701,703,475,189,535,134,122,533,473,132,120,190,534,188,474,133,121,192,531,471,130,118,193,532,472,131,119,191,530,470,129,117,481,541,187,125,113,479,539,185,123,111,480,540,186,124,112,537,477,183,128,116,538,478,184,126,114,127,536,476,182,115,695,698,696,697,604,290,48,391,415,49,602,389,413,291,50,292,603,390,414,293,51,600,387,411,294,52,601,388,412,295,53,599,386,410,610,46,296,397,421,608,47,297,395,419,609,45,298,396,420,42,606,299,393,417,43,607,300,394,418,392,44,605,301,416,674,675,679,684,499,203,143,383,641,141,497,384,639,204,142,205,498,385,640,202,146,495,382,637,200,144,496,380,638,201,145,494,381,636,505,138,194,374,647,503,139,195,375,645,504,140,196,376,646,137,501,197,377,643,135,502,198,378,644,379,136,500,199,642,673,683,677,682,57,82,282,427,402,283,58,425,403,83,281,81,59,426,401,85,278,56,423,398,86,279,54,424,399,84,280,55,422,400,63,288,80,433,408,64,289,78,431,409,65,287,79,432,407,284,62,76,429,404,285,60,77,430,405,428,286,61,75,406,687,686,685,690 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#c633edfa20dc6722982152bc303db7386181f99f3fbdfeb33272ccd5420b69f5, 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 20:35:05 · history