Equation 677 Database

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Magma 7427a9c0a8a1…

magma 7427a9c0a8a1
Size
381
Isomorphism class hash
7427a9c0a8a18322a44b62c881e08a42f9c5b5d3ea5ac47fb671edfd37644d00
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 23:31:16
Display reorder
380,115,136,86,112,165,156,326,329,41,30,248,229,65,55,60,71,76,222,212,202,180,186,275,267,11,17,1,121,140,130,91,96,106,101,170,160,151,145,327,328,324,325,51,46,35,25,253,242,238,234,80,217,207,126,176,280,191,196,290,257,272,261,20,6,295,287,346,372,336,340,331,376,351,355,365,362,116,135,85,111,166,155,302,304,40,31,246,225,66,56,61,70,75,220,210,201,181,185,276,266,10,19,0,120,141,131,90,95,107,102,171,161,150,146,301,300,305,303,50,45,36,26,251,243,235,230,81,216,205,125,175,281,190,195,291,256,271,262,21,5,296,286,345,373,335,341,330,375,350,356,366,360,117,137,88,113,167,157,307,309,43,33,249,226,68,58,63,73,78,224,214,204,182,187,278,268,12,16,3,122,142,132,93,98,108,103,172,162,152,147,308,306,310,311,53,48,38,27,254,244,239,231,83,219,209,127,177,282,192,197,293,258,273,263,22,8,298,289,347,374,337,342,332,377,353,357,368,364,118,138,89,114,168,158,319,321,44,34,247,228,69,59,64,74,79,221,211,200,183,188,277,269,13,15,2,123,143,133,94,99,109,104,173,163,153,148,320,318,322,323,54,49,39,28,252,240,237,233,84,215,206,128,178,283,193,198,292,259,274,264,23,7,297,285,348,370,338,343,333,378,352,358,367,361,119,139,87,110,169,159,315,314,42,32,245,227,67,57,62,72,77,223,213,203,184,189,279,265,14,18,4,124,144,134,92,97,105,100,174,164,154,149,316,317,312,313,52,47,37,29,250,241,236,232,82,218,208,129,179,284,194,199,294,255,270,260,24,9,299,288,349,371,339,344,334,379,354,359,369,363 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#75c864f1b3b5ca4c55a580191a279ecc912d7e894cd469271a5b5b9ceed20bb0, M = {72} 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 23:31:17 · history