Equation 677 Database

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Magma e33924024603…

magma e33924024603
Size
705
Isomorphism class hash
e3392402460309fbac5b827cf1ff256a31ee03c6fe4eb79e78079f6f9e8f463b
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 16:47:58
Display reorder
704,133,132,134,135,136,137,138,139,140,141,142,143,53,536,534,51,535,52,539,49,537,50,538,48,531,59,532,57,533,58,530,55,528,56,529,54,65,523,63,524,64,522,61,526,62,527,60,525,71,521,69,519,70,520,67,517,68,518,66,516,662,663,666,667,233,232,231,228,229,230,238,239,237,234,235,236,437,459,460,435,461,436,458,433,456,434,457,432,465,443,466,441,467,442,464,439,462,440,463,438,449,425,447,423,448,424,445,421,446,422,444,420,455,431,453,429,454,430,451,427,452,428,450,426,687,686,689,688,470,469,468,472,473,471,475,476,474,478,479,477,575,574,570,571,572,573,566,567,568,569,564,565,587,586,583,582,585,584,579,578,581,580,577,576,598,599,595,594,597,596,591,590,593,592,589,588,610,611,607,606,609,608,603,602,604,605,601,600,661,660,669,668,12,14,13,17,15,16,20,18,19,23,21,22,248,267,268,246,269,247,266,251,264,249,265,250,273,243,274,244,275,245,272,242,270,240,271,241,260,4,258,5,259,3,263,1,261,0,262,2,255,10,256,11,257,9,254,6,252,7,253,8,676,677,681,680,197,196,195,192,193,194,202,203,201,198,199,200,316,292,293,317,291,315,288,312,289,313,290,314,298,322,299,323,297,321,294,318,295,319,296,320,281,305,279,303,280,304,277,301,278,302,276,300,287,311,285,309,286,310,283,307,284,308,282,306,665,664,671,670,155,154,153,150,151,152,145,146,144,148,149,147,636,637,639,638,641,640,642,643,644,645,646,647,649,648,651,650,652,653,655,654,657,656,658,659,615,614,617,616,613,612,621,620,622,623,619,618,627,626,628,629,625,624,633,632,634,635,631,630,694,695,698,699,131,130,129,126,127,128,121,122,120,124,125,123,115,89,87,116,88,114,85,118,86,119,84,117,95,113,93,111,94,112,91,109,92,110,90,108,77,100,75,101,76,99,73,96,74,97,72,98,83,106,81,107,82,105,79,102,80,103,78,104,700,701,702,703,207,209,208,205,206,204,215,213,214,211,212,210,355,325,326,356,324,354,328,358,329,359,327,357,331,353,332,351,330,352,334,349,335,350,333,348,367,336,368,337,366,338,370,339,371,340,369,341,365,342,363,343,364,344,361,345,362,346,360,347,692,693,696,697,545,544,543,540,541,542,550,551,549,546,547,548,174,500,498,175,499,176,503,177,501,178,502,179,495,172,496,173,497,171,494,168,492,169,493,170,37,512,38,510,36,511,40,515,41,513,39,514,43,507,44,508,42,509,46,506,47,504,45,505,675,674,678,679,220,219,221,218,216,217,225,226,227,224,222,223,376,403,404,377,402,375,406,372,407,373,405,374,401,382,399,383,400,381,397,378,398,379,396,380,388,415,389,416,387,414,384,418,385,419,386,417,394,413,395,411,393,412,390,409,391,410,392,408,673,672,682,683,554,553,552,556,557,555,563,562,558,560,561,559,488,164,162,486,163,487,167,491,165,489,166,490,159,483,160,484,161,485,158,482,156,480,157,481,187,30,188,31,186,32,190,33,191,34,189,35,185,28,183,29,184,27,181,24,182,25,180,26,685,684,690,691 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#3e7f78778326128ca89bcdb69266df7c07c66aee73c2a2e36b24ead92b52079d, M = {64} 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 16:47:59 · history