Equation 677 Database

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Magma d1c8a16b505b…

magma d1c8a16b505b
Size
381
Isomorphism class hash
d1c8a16b505bd54fe310b9b3f4d4873e11ef28ef3ac8c30db33ca29f148f86e0
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 23:25:25
Display reorder
380,135,130,141,146,120,125,180,185,190,195,200,206,290,295,271,276,280,285,11,16,21,26,1,6,226,231,235,211,216,221,40,45,50,55,31,35,241,246,251,256,261,265,170,175,151,156,160,165,318,319,320,321,322,323,76,86,71,60,66,81,106,116,100,90,95,111,369,344,363,372,335,343,341,356,377,339,136,131,140,145,121,126,181,186,191,196,201,205,291,296,270,275,281,286,10,15,20,25,0,5,225,230,236,210,215,220,41,46,51,56,30,36,240,245,250,255,260,266,173,178,153,158,163,168,325,326,327,328,329,324,77,85,70,61,65,80,105,115,101,91,96,110,365,336,361,373,331,334,332,358,378,337,137,132,142,147,122,127,182,187,192,197,202,207,292,297,272,277,282,287,12,17,22,27,2,7,227,232,237,212,217,222,42,47,52,57,32,37,242,247,252,257,262,267,174,179,154,159,164,169,306,307,308,309,310,311,75,87,72,62,67,83,107,117,102,92,97,112,368,345,360,374,347,348,333,359,379,340,138,133,143,148,123,128,183,188,193,198,203,208,293,298,273,278,283,288,13,18,23,28,3,8,228,233,238,213,218,223,43,48,53,58,33,38,243,248,253,258,263,268,172,177,152,157,162,167,305,301,300,302,303,304,78,88,73,63,68,82,108,118,103,93,98,113,367,351,364,370,350,346,349,357,376,338,139,134,144,149,124,129,184,189,194,199,204,209,294,299,274,279,284,289,14,19,24,29,4,9,229,234,239,214,219,224,44,49,54,59,34,39,244,249,254,259,264,269,171,176,150,155,161,166,315,316,317,312,313,314,79,89,74,64,69,84,109,119,104,94,99,114,366,354,362,371,353,330,352,355,375,342 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#4ff69c35f55aa106c20b4528e074e3f72eddedd150e00069ea529e91bc9e2010, M = {74} 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 23:25:27 · history