Equation 677 Database

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Magma d2972c60da18…

magma d2972c60da18
Size
399
Isomorphism class hash
d2972c60da184fe2a3160d058a2129dcd6478812a70172e9ff845586ab8b1483
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 398) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-07 09:49:34
Display reorder
240,241,242,234,235,236,237,238,239,249,250,251,243,244,245,246,247,248,381,227,252,6,208,228,253,7,209,229,254,8,210,230,255,1,211,231,256,0,212,232,257,2,213,233,258,3,214,225,259,4,215,226,260,5,207,261,15,220,201,262,16,221,202,263,17,222,203,264,9,223,204,265,10,224,205,266,11,216,206,267,12,217,198,268,13,218,199,269,14,219,200,392,386,385,391,124,196,297,333,125,197,298,334,117,189,299,335,118,190,300,336,119,191,301,337,120,192,302,338,121,193,303,339,122,194,304,340,123,195,305,341,180,290,108,326,181,291,109,327,182,292,110,328,183,293,111,329,184,294,112,330,185,295,113,331,186,296,114,332,187,288,115,324,188,289,116,325,384,390,389,383,306,139,281,39,307,140,282,40,308,141,283,41,309,142,284,42,310,143,285,43,311,135,286,44,312,136,287,36,313,137,279,37,314,138,280,38,132,274,315,48,133,275,316,49,134,276,317,50,126,277,318,51,127,278,319,52,128,270,320,53,129,271,321,45,130,272,322,46,131,273,323,47,387,398,397,388,170,25,349,342,162,26,351,344,163,18,353,346,164,19,355,348,165,20,357,350,166,21,359,352,167,22,343,354,168,23,345,356,169,24,347,358,34,367,179,360,35,369,171,362,27,371,172,364,28,373,173,366,29,375,174,368,30,376,175,370,31,361,176,372,32,363,177,374,33,365,178,377,393,395,396,394,85,155,96,54,86,156,97,55,87,157,98,56,88,158,90,57,89,159,91,58,81,160,92,59,82,161,93,60,83,153,94,61,84,154,95,62,148,105,78,63,149,106,79,64,150,107,80,65,151,99,72,66,152,100,73,67,144,101,74,68,145,102,75,69,146,103,76,70,147,104,77,71,380,382,379,378 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 399 = 19 + 5*76, 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#7dbb390eec64c98ee1c1171f4f371cddf97f5d9fe4f94080e4d18eae2edb9ebf, M = the submagma generated by {0} (19 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, 76): MacNeish's product over GF(4) x GF(19); GF(4) = F_2[x]/(x^2 + 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: 21.

last edited by qawbecrdtey at 2026-10-07 09:49:35 · history