Equation 677 Database

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Magma 00da2f1f8371…

magma 00da2f1f8371
Size
705
Isomorphism class hash
00da2f1f8371498618bb397830a50f222135cf66412b49835975caa32b036d50
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 16:22:15
Display reorder
704,513,176,138,161,514,162,177,139,512,163,178,137,164,509,175,141,165,510,173,142,166,511,174,140,136,167,504,159,134,168,505,160,135,169,503,158,170,132,507,155,171,133,508,156,172,131,506,157,151,149,150,154,152,153,146,147,144,145,143,148,661,662,660,663,204,449,410,434,205,435,450,411,203,436,451,412,433,207,452,409,431,208,453,407,432,206,454,408,416,447,210,440,417,448,211,441,418,446,209,442,443,415,213,439,444,413,214,437,445,414,212,438,420,421,419,423,424,422,426,427,428,429,430,425,690,688,691,689,92,532,540,515,90,516,530,541,91,517,531,539,518,95,528,543,519,93,529,544,520,94,527,542,546,538,87,521,547,536,88,522,545,537,89,523,534,549,86,524,535,550,84,525,533,548,85,526,552,553,551,555,556,554,558,559,560,561,562,557,670,668,671,669,12,218,235,252,13,253,219,233,14,251,220,234,255,15,217,238,256,16,215,236,254,17,216,237,230,224,18,258,231,225,19,259,232,226,20,257,223,229,21,261,221,227,22,262,222,228,23,260,243,244,242,239,240,241,249,250,247,245,246,248,679,676,678,677,183,282,290,274,184,272,283,291,182,273,281,292,270,179,285,289,271,180,286,287,269,181,284,288,296,280,189,265,297,278,190,263,298,279,188,264,276,295,185,268,277,293,186,266,275,294,187,267,299,300,301,302,303,304,305,306,310,308,309,307,667,664,666,665,658,657,656,659,650,651,648,649,654,655,652,653,643,642,640,641,647,646,645,644,639,638,636,637,621,620,622,623,613,612,614,615,617,616,618,619,633,632,634,635,624,625,626,627,628,629,630,631,126,127,125,129,130,128,124,122,611,120,121,123,693,695,692,694,29,54,70,37,27,38,55,71,28,36,56,69,40,25,57,66,41,26,58,67,39,24,59,68,61,52,35,43,62,53,33,44,60,51,34,42,48,64,31,46,49,65,32,47,50,63,30,45,82,83,81,78,79,80,73,74,75,76,77,72,701,703,700,702,194,322,331,353,195,354,320,329,196,355,321,330,356,193,318,334,357,191,319,332,358,192,317,333,326,313,200,351,327,311,201,352,328,312,202,350,316,325,199,347,314,323,197,348,315,324,198,349,340,338,339,336,337,335,346,344,341,342,343,345,697,699,696,698,118,486,496,468,119,469,487,494,117,467,485,495,471,114,489,492,472,115,490,493,470,116,488,491,502,484,109,474,500,482,110,475,501,483,108,473,480,498,112,477,481,499,113,478,479,497,111,476,462,463,461,465,466,464,460,458,455,456,457,459,674,672,675,673,0,397,370,393,2,394,395,368,1,392,396,369,389,4,400,366,390,5,398,367,391,3,399,365,361,403,7,384,359,401,8,385,360,402,6,383,406,364,10,387,404,362,11,388,405,363,9,386,373,371,372,376,374,375,379,377,381,382,380,378,683,681,680,682,103,589,608,579,104,580,587,609,102,578,588,610,575,106,592,607,576,107,590,605,577,105,591,606,599,595,101,585,600,593,99,586,601,594,100,584,598,602,97,581,596,603,98,582,597,604,96,583,566,567,568,565,563,564,572,573,570,571,569,574,685,686,684,687 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#2e8e4ac0a437874a6303a2bb1c968f3f1df955f15fe5de36e1349d884d5d267c, 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 16:22:17 · history