Equation 677 Database

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Magma 5dc19e4a7b38…

magma 5dc19e4a7b38
Size
381
Isomorphism class hash
5dc19e4a7b3886220571f6a2dcd3846321f9e2920c1adeb81dd212f37761b332
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 380) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:33:28
Display reorder
380,209,199,219,229,239,189,56,57,58,59,54,55,301,300,302,303,304,305,269,279,289,299,249,258,147,148,149,144,145,146,52,53,48,49,50,51,152,153,154,155,150,151,137,132,133,134,135,136,140,141,142,143,138,139,215,225,235,185,195,205,295,285,245,254,265,275,375,356,363,368,355,357,354,343,342,379,204,194,214,224,234,184,127,128,129,130,131,126,307,308,309,310,311,306,264,274,284,294,244,253,72,73,74,75,76,77,125,120,121,122,123,124,78,79,80,81,82,83,29,24,25,26,27,28,32,33,34,35,30,31,213,223,233,183,193,203,293,283,243,252,263,273,370,346,361,369,338,332,337,353,352,374,202,192,212,222,232,182,112,113,108,109,110,111,321,322,323,318,319,320,262,272,282,292,242,259,156,157,158,159,160,161,116,117,118,119,114,115,162,163,164,165,166,167,66,67,68,69,70,71,60,61,62,63,64,65,211,221,231,180,190,201,291,280,240,250,260,270,371,358,367,360,344,339,345,350,351,373,207,197,217,227,237,187,89,84,85,86,87,88,326,327,328,329,324,325,267,277,287,297,247,256,47,42,43,44,45,46,94,95,90,91,92,93,38,39,40,41,36,37,168,169,170,171,172,173,175,176,177,178,179,174,218,228,238,188,198,208,298,288,248,257,268,278,378,340,366,365,359,341,330,348,347,377,206,196,216,226,236,186,10,11,6,7,8,9,317,312,313,314,315,316,266,276,286,296,246,255,14,15,16,17,12,13,3,4,5,1,0,2,22,23,18,19,20,21,97,98,99,100,101,96,105,106,107,102,103,104,210,220,230,181,191,200,290,281,241,251,261,271,372,336,362,364,349,335,331,334,333,376 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 381 = 1 + 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#83cf1f35d4fb7256f5d65d48e163e6c0239fd3c4b75a82ae41fd7ea0fe92a1c5, M = {66} 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: 51.

last edited by qawbecrdtey at 2026-10-01 23:33:29 · history