Equation 677 Database

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Magma c802d37198b2…

magma c802d37198b2
Size
381
Isomorphism class hash
c802d37198b259865536b270fbc84d57a8f78565241f638be3b16fc638009748
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 23:26:15
Display reorder
380,137,136,138,139,140,141,149,132,133,134,135,1,126,127,128,129,130,131,190,195,201,206,180,185,165,170,175,151,155,160,124,125,120,121,122,123,275,280,286,291,296,270,255,261,266,240,245,250,236,210,215,220,225,231,324,325,326,327,328,329,144,146,142,145,147,143,354,352,336,365,339,370,358,353,362,375,91,119,92,93,90,89,105,100,101,102,103,104,94,95,96,97,98,99,193,198,203,208,183,188,168,173,178,153,158,163,115,116,117,112,113,114,278,284,289,294,298,273,259,264,269,244,249,254,239,214,219,224,228,233,318,319,320,321,322,323,109,111,107,110,106,108,350,334,348,368,349,373,356,351,364,378,73,76,0,148,74,75,69,70,71,72,67,68,83,84,85,86,87,88,191,196,200,205,181,186,166,171,176,150,156,161,81,82,77,78,79,80,276,281,285,290,295,271,256,260,265,241,246,251,235,211,216,221,226,230,302,303,304,305,301,300,2,4,6,3,5,7,338,337,346,367,332,372,357,347,361,377,16,15,17,18,13,14,30,25,26,27,28,29,19,20,21,22,23,24,194,199,204,209,184,189,169,174,179,154,159,164,40,41,42,37,38,39,279,283,288,293,299,274,258,263,268,243,248,253,238,213,218,223,229,234,308,309,310,311,306,307,34,36,32,35,31,33,343,331,341,366,342,371,355,340,363,376,59,58,60,55,56,57,12,9,8,118,10,11,54,49,50,51,52,53,192,197,202,207,182,187,167,172,177,152,157,162,43,44,45,46,47,48,277,282,287,292,297,272,257,262,267,242,247,252,237,212,217,222,227,232,316,317,312,313,314,315,62,64,66,63,65,61,330,344,345,369,333,374,359,335,360,379 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#50609e522fd5f79e53ac56beafcb5b424f2d261582798854b4ac2a2a84486b65, 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 23:26:16 · history