Equation 677 Database

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Magma 2e016069036a…

magma 2e016069036a
Size
381
Isomorphism class hash
2e016069036abe7ca2526241cefe3027f4db8cca6b5b89b836725e5f030cdbc5
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 23:46:26
Display reorder
380,134,133,129,130,131,132,128,126,127,274,283,294,113,108,109,110,111,112,237,212,217,222,227,232,300,302,303,304,305,301,252,257,262,267,242,247,162,167,172,177,152,157,187,192,197,202,207,182,121,122,123,124,125,120,142,147,137,277,287,297,114,118,115,116,117,119,350,343,347,367,344,333,371,357,377,360,74,73,75,76,77,72,78,79,80,270,284,292,67,68,69,70,71,66,235,211,216,221,226,231,308,309,310,306,311,307,250,255,260,265,241,246,161,165,170,175,151,156,186,191,195,200,205,181,63,64,65,60,61,62,141,146,136,276,286,296,56,54,57,58,59,55,351,338,349,368,331,339,373,356,378,363,104,103,105,106,107,102,81,82,83,273,282,293,97,98,99,100,101,96,238,213,218,223,228,233,320,321,322,323,318,319,253,258,263,268,243,248,163,168,173,178,153,158,188,193,198,203,208,183,93,94,95,90,91,92,143,148,138,278,288,298,86,84,87,88,89,85,352,335,346,369,340,341,374,358,379,364,46,45,47,42,43,44,8,1,0,271,281,291,36,37,38,39,40,41,236,210,215,220,225,230,316,317,312,313,314,315,251,256,261,266,240,245,160,166,171,176,150,155,185,190,196,201,206,180,6,7,2,3,4,5,140,145,135,275,285,295,51,49,52,53,48,50,354,342,348,366,330,334,370,355,375,361,19,18,20,15,16,17,33,34,35,272,280,290,9,10,11,12,13,14,239,214,219,224,229,234,329,324,325,326,327,328,254,259,264,269,244,249,164,169,174,179,154,159,189,194,199,204,209,184,31,32,27,28,29,30,144,149,139,279,289,299,24,22,25,26,21,23,353,336,345,365,337,332,372,359,376,362 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#dc50bff4268d4e886a12bccb100fd4b53117610e2c07e48d4c792db14c6c3b47, M = {73} 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 23:46:27 · history