Equation 677 Database

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Magma aca25c242d13…

magma aca25c242d13
Size
705
Isomorphism class hash
aca25c242d13c50b2dc889e529b3360bce6eca68283e0adf976faa2eec85f119
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 15:22:08
Display reorder
660,586,585,584,111,595,546,545,544,112,555,566,565,564,113,575,646,644,645,110,655,604,606,605,108,615,625,626,109,635,624,484,485,117,486,495,504,505,118,506,515,524,525,119,526,535,465,464,116,466,475,425,424,114,436,437,445,444,115,446,455,691,686,698,702,598,591,594,53,599,558,551,554,51,559,578,571,574,52,579,658,654,651,49,659,614,618,611,50,619,631,638,48,639,634,494,491,59,499,498,514,511,57,519,518,534,531,58,539,538,471,474,55,479,478,428,429,56,439,438,451,454,54,459,458,687,692,685,697,162,292,170,24,416,163,293,168,25,414,164,291,169,26,415,165,173,288,27,419,171,166,289,28,417,290,167,29,418,172,176,298,30,160,411,174,299,31,161,412,175,297,32,159,413,294,179,33,156,410,295,177,34,157,408,296,178,35,158,409,667,679,684,677,192,332,215,248,278,193,330,213,246,276,194,331,214,247,277,195,211,335,251,281,212,196,333,249,279,334,197,250,280,210,206,327,243,198,284,204,328,244,199,282,205,329,245,200,283,326,209,242,201,287,324,207,240,202,285,325,208,241,203,286,676,666,664,668,597,590,582,91,588,557,550,542,92,548,577,570,562,90,568,657,642,650,94,648,602,617,610,95,608,630,637,93,628,622,481,490,89,497,488,501,510,87,517,508,520,530,88,537,528,470,462,85,477,468,434,432,86,431,426,450,441,84,457,448,700,689,696,699,580,587,593,224,596,541,547,553,222,556,560,567,573,223,576,640,653,647,227,656,613,601,607,225,616,627,621,226,636,633,493,487,219,483,496,513,507,220,503,516,533,527,221,523,536,467,473,218,460,476,433,435,216,423,430,447,453,217,443,456,695,688,690,694,592,589,583,238,581,552,549,543,239,540,572,569,563,237,561,652,643,649,234,641,603,612,609,235,600,629,632,236,620,623,482,489,229,492,480,502,509,230,512,500,522,529,228,532,521,469,463,232,472,461,427,422,233,421,420,449,442,231,452,440,693,704,703,701,81,368,344,40,60,82,366,342,41,61,83,367,343,39,62,80,347,371,36,63,345,78,369,37,64,370,79,38,65,346,339,363,46,72,66,340,364,47,73,67,341,365,45,74,68,362,338,42,75,69,360,336,43,76,70,361,337,44,77,71,682,672,665,670,137,392,146,18,122,135,390,144,19,120,136,391,145,20,121,133,149,395,21,125,147,134,393,22,123,394,132,23,124,148,152,387,16,143,128,150,388,17,141,126,151,389,15,142,127,386,155,12,139,131,384,153,13,140,129,385,154,14,138,130,681,675,674,662,356,190,380,300,269,354,191,378,301,267,355,189,379,302,268,359,383,186,303,265,381,357,187,304,266,188,358,305,264,382,375,181,306,351,275,376,182,307,352,273,377,180,308,353,274,184,374,309,350,271,185,372,310,348,272,183,373,311,349,270,671,669,683,673,404,6,320,96,260,402,7,318,97,258,403,8,319,98,259,407,323,9,99,263,321,405,10,100,261,11,406,101,262,322,315,4,102,399,255,316,5,103,400,256,317,3,104,401,257,1,314,105,398,254,0,312,106,396,252,2,313,107,397,253,678,680,661,663 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#15e0002a5ecb0f8e7ea13fca6591bd645ffece494b3bd71abe8f3bbcdb21ed68, M = {60} in E, B = magma#9878faa9b07066f62fc077f7c99df5b1f6f079c61c0cd7e7f5bbdb9bc181adbc. 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 15:22:09 · history