Equation 677 Database

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Magma 374b5e31fc09…

magma 374b5e31fc09
Size
705
Isomorphism class hash
374b5e31fc0928442bd1ac4c7582f6d45fb7dae9a7ea504bb1241325ab66cd82
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 21:24:33
Display reorder
660,327,406,214,312,329,325,407,215,310,330,326,408,216,311,328,409,217,315,332,323,410,324,218,313,333,411,322,219,314,331,307,212,318,404,335,213,316,405,308,336,211,317,403,309,334,321,208,400,306,338,319,209,401,304,339,320,210,402,305,337,663,664,662,671,164,442,421,358,175,162,443,422,359,176,163,444,423,360,174,445,420,361,171,160,446,161,418,362,172,447,159,419,363,173,356,412,170,440,181,413,168,441,357,182,414,169,439,355,180,166,415,436,352,177,167,416,437,353,178,165,417,438,354,179,687,690,685,686,562,617,245,97,490,563,618,246,95,491,564,619,244,96,492,620,248,93,493,565,621,566,249,94,494,622,567,247,92,495,88,251,560,615,488,252,561,616,86,489,250,559,614,87,487,556,254,611,91,484,557,255,612,89,485,558,253,613,90,486,672,667,665,668,430,377,32,5,368,431,378,33,6,369,432,376,31,4,367,380,35,0,364,433,381,434,36,2,365,379,435,34,3,366,11,30,428,383,374,28,429,384,12,375,29,427,382,10,373,424,26,386,7,370,425,27,387,8,371,426,25,385,9,372,674,675,676,683,526,581,45,394,593,527,582,43,395,594,528,583,44,396,595,584,48,397,596,529,585,530,46,398,597,586,531,47,399,598,392,40,524,579,591,41,525,580,393,592,42,523,578,391,590,520,39,575,388,587,521,37,576,389,588,522,38,577,390,589,669,666,670,661,466,234,84,347,221,467,232,85,348,222,468,233,83,346,220,237,80,350,224,469,235,470,81,351,225,236,471,82,349,223,345,75,464,240,227,76,465,238,343,228,74,463,239,344,226,460,78,243,341,230,461,79,241,342,231,462,77,242,340,229,698,694,693,695,201,574,190,629,1,642,643,191,640,641,644,645,189,646,647,648,193,650,651,649,652,653,194,654,655,656,657,192,658,659,624,196,202,569,184,197,203,570,625,185,195,204,568,623,183,205,199,572,627,187,206,200,573,628,188,207,198,571,626,186,702,701,704,703,73,99,72,110,134,630,100,70,111,631,633,98,71,112,632,102,68,113,634,635,103,637,69,114,636,101,638,67,115,639,116,63,142,105,140,61,143,106,117,138,62,141,104,118,139,145,66,108,119,136,146,64,109,120,137,144,65,107,121,135,696,699,700,697,281,605,56,454,293,282,606,57,455,294,280,607,55,456,292,608,59,457,296,284,609,285,60,458,297,610,283,58,459,295,452,54,287,603,299,52,288,604,453,300,53,286,602,451,298,290,50,599,448,302,291,51,600,449,303,289,49,601,450,301,682,679,673,677,478,154,123,502,550,479,155,124,503,551,480,153,122,504,552,157,126,505,553,481,158,482,127,506,554,156,483,125,507,555,500,129,476,152,548,130,477,150,501,549,128,475,151,499,547,472,132,148,496,544,473,133,149,497,545,474,131,147,498,546,681,678,680,684,265,514,17,538,278,266,515,18,539,279,267,516,16,540,277,517,13,541,274,264,518,262,14,542,275,519,263,15,543,276,536,23,256,512,269,24,257,513,537,270,22,258,511,535,268,259,19,508,532,272,260,20,509,533,273,261,21,510,534,271,688,691,692,689 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#ef4a4f27352a122a7b1088a6208971ffd57fb3858716fe27bd37fbc92d64744c, 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 21:24:34 · history