Equation 677 Database

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Magma 882018683bf3…

magma 882018683bf3
Size
705
Isomorphism class hash
882018683bf38f418f299fbb0cebf7ef9341067538a7b18f744fd39e0c4b29aa
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 16:39:45
Display reorder
660,108,593,370,425,413,414,594,109,371,426,595,415,110,372,427,416,107,596,373,428,105,417,597,374,429,418,106,598,375,430,411,114,591,368,423,412,115,592,369,424,367,410,116,590,422,113,407,587,364,419,111,408,588,365,420,112,409,589,366,421,661,664,663,671,186,449,183,228,10,11,450,184,181,226,451,12,185,182,227,9,189,452,179,231,187,7,453,180,229,8,188,454,178,230,0,192,447,174,223,2,190,448,172,224,173,3,191,446,225,195,4,443,177,222,193,5,444,175,220,194,6,445,176,221,688,690,685,686,140,302,314,327,329,330,303,138,315,325,301,328,139,313,326,332,136,298,310,323,137,333,299,311,324,331,135,300,312,322,335,131,293,305,318,336,129,294,306,316,304,334,130,292,317,134,338,296,308,321,132,339,297,309,319,133,337,295,307,320,667,662,669,665,88,485,203,240,248,249,486,89,204,238,487,247,87,202,239,244,91,488,206,243,92,245,489,207,241,246,90,490,205,242,254,86,483,201,235,255,84,484,199,236,200,253,85,482,237,82,250,479,197,234,83,251,480,198,232,81,252,481,196,233,675,677,673,678,24,437,257,214,569,570,438,22,258,215,439,571,23,256,216,572,20,440,260,217,21,573,441,261,218,574,19,442,259,219,567,15,435,263,212,568,13,436,264,213,262,566,14,434,211,18,563,431,266,208,16,564,432,267,209,17,565,433,265,210,672,668,670,666,124,93,461,557,545,546,94,125,462,558,95,547,123,463,559,548,127,96,464,560,128,549,97,465,561,550,126,98,466,562,543,122,99,459,555,544,120,100,460,556,458,542,121,101,554,118,539,102,455,551,119,540,103,456,552,117,541,104,457,553,694,698,697,693,49,50,31,394,629,643,642,47,641,640,644,647,48,646,645,651,45,649,650,648,46,655,653,654,652,659,44,657,658,656,627,40,51,32,389,628,38,52,33,390,34,626,39,53,388,43,623,54,35,392,41,624,55,36,393,42,625,56,37,391,701,702,704,703,271,497,509,1,153,630,498,272,510,631,499,633,273,511,632,634,270,500,512,635,268,636,501,513,637,638,269,502,514,639,159,277,495,507,26,157,278,496,508,27,506,158,279,494,25,276,155,491,503,29,274,156,492,504,30,275,154,493,505,28,696,700,699,695,72,581,397,473,361,362,582,73,395,474,583,363,74,396,475,360,71,584,400,476,69,358,585,398,477,359,70,586,399,478,352,78,579,403,471,353,79,580,401,472,402,354,80,578,470,77,355,575,406,467,75,356,576,404,468,76,357,577,405,469,684,676,680,682,287,605,165,382,521,522,606,288,163,383,607,523,286,164,384,524,290,608,161,385,291,525,609,162,386,526,289,610,160,387,519,285,603,171,380,520,283,604,169,381,170,518,284,602,379,281,515,599,167,376,282,516,600,168,377,280,517,601,166,378,681,674,679,683,63,148,533,617,349,350,149,64,534,618,147,351,65,535,619,348,66,151,536,620,67,346,152,537,621,347,68,150,538,622,340,61,146,531,615,341,62,144,532,616,530,342,60,145,614,57,343,142,527,611,58,344,143,528,612,59,345,141,529,613,687,692,691,689 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#3866b47acdf4717a31e27879d6448be53ada0b89c1671a7aec66e55c44000764, 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 16:39:47 · history