Equation 677 Database

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Magma a53362ce325f…

magma a53362ce325f
Size
705
Isomorphism class hash
a53362ce325fb3ca2d243b5bed352dfce600576c059c95eefd465b1fc3cb4d6c
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 16:42:13
Display reorder
660,54,320,171,358,127,128,318,55,172,359,319,126,56,173,357,130,57,316,174,361,58,131,317,175,362,59,129,315,176,360,52,326,169,125,356,53,324,170,123,354,51,325,168,124,355,322,48,165,121,352,323,49,166,122,353,321,50,167,120,351,672,664,663,665,478,406,41,19,634,635,407,479,39,20,405,633,477,40,18,637,481,409,37,22,482,638,410,38,23,480,636,408,36,21,476,404,47,632,25,474,402,45,630,26,475,403,46,631,24,400,472,43,628,35,401,473,44,629,29,399,471,42,627,32,687,685,686,692,254,276,184,265,346,347,277,252,185,266,278,345,253,183,264,349,250,275,187,261,251,350,273,188,262,249,348,274,186,263,245,267,182,344,256,243,268,180,342,257,244,269,181,343,255,270,248,178,340,259,271,246,179,341,260,272,247,177,339,258,662,666,670,661,466,586,115,370,394,395,587,467,116,371,585,393,465,114,369,397,469,589,118,373,470,398,590,119,374,468,396,588,117,372,464,584,113,392,368,462,582,111,390,366,463,583,112,391,367,580,460,109,388,364,581,461,110,389,365,579,459,108,387,363,678,674,681,675,574,502,17,85,514,515,503,575,15,86,501,513,573,16,84,517,577,505,13,88,578,518,506,14,89,576,516,504,12,87,572,500,0,512,91,570,498,2,510,92,571,499,1,511,90,496,568,34,508,94,497,569,28,509,95,495,567,31,507,93,671,669,667,668,442,203,163,189,418,419,201,443,164,190,202,417,441,162,191,421,445,206,159,192,446,422,204,160,193,444,420,205,161,194,440,209,154,416,195,438,207,155,414,196,439,208,153,415,197,212,436,157,412,198,210,437,158,413,199,211,435,156,411,200,696,699,697,695,134,225,74,645,235,236,226,132,72,646,227,234,133,73,647,654,653,652,77,655,657,658,656,75,659,648,650,649,76,651,137,228,80,238,643,135,229,78,239,644,136,230,79,237,642,231,140,83,241,639,232,138,81,242,640,233,139,82,240,641,704,702,703,701,538,151,5,382,610,611,152,539,3,383,150,609,537,4,381,613,541,147,8,385,542,614,148,6,386,540,612,149,7,384,536,142,11,608,380,534,143,9,606,378,535,141,10,607,379,145,532,33,604,376,146,533,27,605,377,144,531,30,603,375,698,694,693,700,526,430,107,454,598,599,431,527,105,455,429,597,525,106,453,601,529,433,103,457,530,602,434,104,458,528,600,432,102,456,524,428,98,596,452,522,426,96,594,450,523,427,97,595,451,424,520,101,592,448,425,521,99,593,449,423,519,100,591,447,679,677,676,682,296,550,305,622,288,289,551,294,303,623,549,290,295,304,621,287,292,553,308,625,293,285,554,306,626,291,286,552,307,624,302,548,311,279,620,300,546,309,280,618,301,547,310,281,619,544,298,314,282,616,545,299,312,283,617,543,297,313,284,615,684,683,680,673,490,219,64,332,562,563,220,491,65,330,221,561,489,63,331,565,493,222,60,328,494,566,223,61,329,492,564,224,62,327,488,217,70,560,338,486,218,71,558,336,487,216,69,559,337,213,484,66,556,334,214,485,67,557,335,215,483,68,555,333,688,691,689,690 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#3a1e3dea02005faeb7a32ea89e0ebcd7060d0e295c5a20add7fb441719113d75, 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 16:42:14 · history