Equation 677 Database

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Magma 5162bc762c02…

magma 5162bc762c02
Size
705
Isomorphism class hash
5162bc762c02928934ca2e905f5da971fbbdd74068b4f2cccdc989c63d82f9b7
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 19:17:34
Display reorder
660,249,434,470,262,446,263,250,432,468,444,261,251,433,469,445,258,248,437,473,449,259,246,435,471,447,260,247,436,472,448,240,429,465,253,441,241,430,466,254,442,242,431,467,252,443,243,428,464,256,440,244,426,462,257,438,245,427,463,255,439,665,666,672,668,128,614,554,8,100,6,126,612,552,101,7,127,613,553,99,11,131,617,557,96,9,129,615,555,97,10,130,616,556,98,123,609,549,3,106,124,610,550,4,107,125,611,551,5,105,122,608,548,2,102,120,606,546,1,103,121,607,547,0,104,689,690,685,687,398,332,458,287,482,285,396,330,456,480,286,397,331,457,481,283,401,335,461,485,284,399,333,459,483,282,400,334,460,484,393,327,453,278,477,394,328,454,276,478,395,329,455,277,479,392,326,452,281,476,390,324,450,279,474,391,325,451,280,475,671,669,663,667,148,374,506,184,542,185,149,372,504,540,183,147,373,505,541,180,144,377,509,545,181,145,375,507,543,182,146,376,508,544,154,369,501,190,537,155,370,502,191,538,153,371,503,189,539,150,368,500,186,536,151,366,498,187,534,152,367,499,188,535,674,680,673,677,494,410,157,141,362,142,492,408,158,360,143,493,409,156,361,140,497,413,160,365,138,495,411,161,363,139,496,412,159,364,489,405,163,132,357,490,406,164,133,358,491,407,162,134,359,488,404,166,135,356,486,402,167,136,354,487,403,165,137,355,664,661,670,662,578,28,265,60,318,61,576,29,266,319,62,577,27,264,320,63,581,24,268,321,64,579,25,269,322,65,580,26,267,323,573,34,271,66,316,574,35,272,67,317,575,33,270,68,315,572,30,274,69,312,570,31,275,70,313,571,32,273,71,314,693,695,698,694,647,644,646,118,645,119,639,638,636,637,117,643,640,642,641,114,659,656,658,657,115,651,649,650,648,116,655,653,654,652,621,337,343,109,352,622,338,344,110,353,623,336,342,108,351,620,340,346,112,348,618,341,347,113,349,619,339,345,111,350,701,702,704,703,530,629,518,48,628,49,528,624,516,625,50,529,627,517,626,51,533,635,521,634,52,531,631,519,630,53,532,633,520,632,525,176,513,54,173,526,174,514,55,171,527,175,515,56,172,524,179,512,57,169,522,177,510,58,170,523,178,511,59,168,700,699,697,696,386,590,234,12,303,13,384,588,235,304,14,385,589,236,305,15,389,593,237,302,16,387,591,238,300,17,388,592,239,301,381,585,232,18,309,382,586,233,19,310,383,587,231,20,311,380,584,228,21,308,378,582,229,22,306,379,583,230,23,307,684,678,675,681,602,82,422,36,85,37,600,83,420,86,38,601,81,421,84,39,605,78,425,88,40,603,79,423,89,41,604,80,424,87,597,73,417,42,91,598,74,418,43,92,599,72,419,44,90,596,76,416,45,94,594,77,414,46,95,595,75,415,47,93,679,683,682,676,194,216,206,296,566,294,192,217,204,564,295,193,218,205,565,299,197,219,209,569,297,195,220,207,567,298,196,221,208,568,200,222,212,291,561,198,223,210,292,562,199,224,211,293,563,203,225,215,290,560,201,226,213,288,558,202,227,214,289,559,686,688,692,691 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#9741437d1171904ffa64043ea6d962aefa7dc37d5417f733d15a56c498f18cdb, 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 19:17:35 · history