Equation 677 Database

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Magma cc742ac0fa50…

magma cc742ac0fa50
Size
381
Isomorphism class hash
cc742ac0fa50c7861b3edf4626676c666d9e273a3b81c1257e63e0da4df59688
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 23:36:11
Display reorder
380,51,60,56,70,65,276,201,191,196,185,175,180,161,151,156,171,165,296,125,130,136,141,290,146,328,329,327,325,326,324,36,26,31,271,40,45,91,280,96,76,80,85,1,6,11,19,266,22,226,230,221,210,215,205,120,111,115,105,285,101,235,240,246,250,256,261,355,366,346,370,360,336,350,330,341,376,52,62,57,72,67,277,202,192,197,187,177,182,162,152,157,172,167,297,127,132,137,142,292,147,315,316,317,312,313,314,37,27,32,272,42,47,92,282,97,77,82,87,2,7,12,16,267,21,227,232,222,212,217,207,122,112,117,107,287,102,237,242,247,252,257,262,357,367,347,372,362,337,352,332,342,377,54,64,59,74,69,279,204,194,199,189,179,184,164,154,159,174,169,299,129,134,139,144,294,149,307,308,306,310,311,309,39,29,34,274,44,49,94,284,99,79,84,89,4,9,14,18,269,24,229,234,224,214,219,209,124,114,119,109,289,104,239,244,249,254,259,264,359,369,349,374,364,339,354,334,343,379,50,61,55,71,66,275,200,190,195,186,176,181,160,150,155,170,166,295,126,131,135,140,291,145,305,303,304,302,301,300,35,25,30,270,41,46,90,281,95,75,81,86,0,5,10,15,265,20,225,231,220,211,216,206,121,110,116,106,286,100,236,241,245,251,255,260,356,365,345,371,361,335,351,331,340,375,53,63,58,73,68,278,203,193,198,188,178,183,163,153,158,173,168,298,128,133,138,143,293,148,318,319,320,321,322,323,38,28,33,273,43,48,93,283,98,78,83,88,3,8,13,17,268,23,228,233,223,213,218,208,123,113,118,108,288,103,238,243,248,253,258,263,358,368,348,373,363,338,353,333,344,378 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 = {75} 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 23:36:12 · history