Equation 677 Database

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Magma 14c44cb6fa17…

magma 14c44cb6fa17
Size
595
Isomorphism class hash
14c44cb6fa1741c832b035b2b948308b9f185116929379a3813a14a9215cf429
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 594) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-08 10:20:25
Display reorder
276,278,277,280,281,279,272,270,271,273,274,275,368,367,369,370,365,366,489,488,490,485,486,487,404,403,405,406,401,402,555,556,577,583,594,85,84,87,88,89,86,104,103,102,106,107,105,137,136,135,134,132,133,220,219,221,217,218,216,181,180,182,184,185,183,91,90,92,94,95,93,177,179,178,176,174,175,256,255,257,254,252,253,234,235,236,238,239,237,494,493,495,496,491,492,394,393,389,390,391,392,362,361,363,364,359,360,395,400,396,397,398,399,350,349,351,352,347,348,372,371,373,374,375,376,465,464,466,461,462,463,539,520,554,529,514,544,548,531,519,593,588,560,571,576,566,582,97,96,99,100,101,98,6,8,7,11,9,10,57,59,58,54,55,56,204,206,205,207,208,209,233,232,231,230,228,229,192,194,193,195,196,197,71,70,69,67,68,66,244,243,245,242,241,240,61,60,62,64,65,63,427,426,428,429,430,425,380,379,381,382,377,378,327,326,328,329,324,325,320,319,321,322,323,318,312,317,313,314,315,316,437,442,438,439,440,441,457,456,458,459,460,455,538,524,551,528,513,542,547,534,518,592,587,559,570,575,565,581,119,118,115,116,114,117,160,159,161,156,157,158,82,81,83,79,80,78,138,140,139,141,142,143,18,20,19,21,22,23,213,215,214,210,211,212,126,128,127,131,129,130,265,264,266,269,267,268,48,50,49,51,52,53,306,311,307,308,309,310,432,431,433,434,435,436,499,498,500,501,502,497,471,470,472,467,468,469,451,450,452,453,454,449,422,421,423,424,419,420,342,341,343,344,345,346,537,521,552,526,512,543,545,532,516,591,584,561,567,574,563,578,1,2,5,3,4,0,149,148,147,145,146,144,203,202,201,200,198,199,72,74,73,75,76,77,123,125,124,120,121,122,24,26,25,27,28,29,108,110,109,113,111,112,258,260,259,262,263,261,16,15,17,13,14,12,477,476,478,473,474,475,411,410,412,407,408,409,503,508,504,505,506,507,447,446,448,443,444,445,384,383,385,386,387,388,283,287,282,284,285,286,353,358,354,355,356,357,535,522,550,527,510,540,549,530,515,589,586,558,568,573,562,580,151,150,153,154,155,152,35,34,33,31,32,30,47,46,45,44,42,43,166,165,167,163,164,162,224,223,222,227,225,226,39,41,40,36,37,38,190,189,191,186,187,188,251,250,249,246,247,248,170,169,168,173,171,172,295,294,296,297,298,299,415,414,416,417,418,413,340,339,337,338,336,509,479,484,480,481,482,483,304,303,305,300,301,302,333,332,334,335,330,331,289,288,290,291,292,293,536,523,553,525,511,541,546,533,517,590,585,557,569,572,564,579 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 595 = 35 + 5*112, 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, 5, B) with E = magma#53d992532d406ee1a16d046074f6b11dc06c8f5c6df8c27dc9277719dd794878, M = the submagma generated by {6, 36} (35 elements) in E, B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5. 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(5, 112): MacNeish's product over GF(16) x GF(7); GF(16) = F_2[x]/(x^4 + 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: 85.

last edited by qawbecrdtey at 2026-10-08 10:20:26 · history