Equation 677 Database

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Magma 3cc076bd012a…

magma 3cc076bd012a
Size
381
Isomorphism class hash
3cc076bd012a553cf3a78fc63ba646bd973589d48659ab14f64d40cb9feac3a9
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 23:35:32
Display reorder
380,178,188,183,173,163,168,258,248,253,243,232,237,93,298,98,78,83,88,283,288,278,268,273,263,203,193,198,218,207,213,293,53,58,62,68,73,153,158,148,138,143,133,16,17,15,19,228,18,28,33,223,43,48,38,312,313,314,315,316,317,103,108,113,118,123,128,353,363,338,358,343,378,374,348,333,368,179,189,184,174,164,169,259,249,254,244,233,238,94,299,99,79,84,89,284,289,279,269,274,264,204,194,199,219,209,214,294,54,59,63,69,74,154,159,149,139,144,134,21,22,20,24,229,23,29,34,224,44,49,39,318,319,320,321,322,323,104,109,114,119,124,129,354,364,339,359,344,379,373,349,334,369,177,187,182,172,162,167,256,246,251,240,231,236,92,297,97,77,82,87,281,286,276,266,270,261,202,192,197,217,208,212,290,51,56,61,67,71,152,157,147,137,142,132,6,7,5,9,225,8,27,32,222,42,47,37,302,301,300,305,303,304,102,107,112,117,122,127,352,362,337,355,340,377,372,346,332,365,176,185,180,170,161,165,257,247,252,242,234,239,91,295,95,75,80,85,282,287,277,265,272,260,201,190,196,216,205,210,292,52,57,60,65,70,150,156,146,135,140,131,11,12,10,14,227,13,26,31,220,41,45,36,309,310,311,306,307,308,100,106,111,116,120,126,350,361,335,357,342,376,371,347,331,367,175,186,181,171,160,166,255,245,250,241,230,235,90,296,96,76,81,86,280,285,275,267,271,262,200,191,195,215,206,211,291,50,55,64,66,72,151,155,145,136,141,130,2,3,4,1,226,0,25,30,221,40,46,35,328,329,327,325,326,324,101,105,110,115,121,125,351,360,336,356,341,375,370,345,330,366 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#8e237b368ce49904371f47a0bbc192c3f49c4a8da81336b4c06fd9fdc3a5d75d, 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 23:35:32 · history