Equation 677 Database

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Magma 587194d7ddb2…

magma 587194d7ddb2
Size
381
Isomorphism class hash
587194d7ddb232fecff219ccce1a7cfbfe16749342f70dc52f1a0f8dc13b1e55
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 23:36:30
Display reorder
380,29,41,34,11,326,4,52,22,45,59,57,39,27,35,9,327,5,53,23,46,58,40,28,33,10,328,3,51,21,47,20,36,323,54,43,32,24,6,2,13,37,18,324,55,14,44,30,25,7,1,38,19,325,56,12,42,31,26,8,0,15,16,49,50,48,17,345,353,344,335,370,360,359,377,346,347,150,127,120,164,309,157,138,175,134,145,146,128,151,121,162,307,158,139,176,132,144,126,152,122,163,308,156,140,174,133,173,125,322,143,129,147,177,159,155,166,123,171,310,141,167,130,148,178,160,153,124,172,306,142,165,131,149,179,161,154,168,169,135,136,137,170,365,352,364,373,363,374,351,334,375,379,258,270,295,240,311,265,284,254,277,288,289,271,259,296,241,312,266,282,252,278,290,272,260,294,242,313,264,283,253,276,249,297,314,286,275,293,256,267,263,245,298,250,315,287,243,273,291,257,268,261,299,251,316,285,244,274,292,255,269,262,247,248,281,279,280,246,366,357,358,338,337,356,331,330,336,367,231,208,201,213,300,238,190,227,183,197,195,209,232,202,214,302,239,191,225,184,196,207,233,203,215,301,237,189,226,185,222,206,304,192,181,199,229,211,236,218,204,223,305,193,216,182,200,230,212,234,205,224,303,194,217,180,198,228,210,235,220,221,187,188,186,219,362,378,349,355,348,350,333,361,371,372,95,69,65,106,318,99,83,117,76,87,88,70,93,63,107,319,100,81,118,77,89,71,94,64,105,317,101,82,119,75,115,67,321,85,74,60,90,104,97,108,68,116,329,86,109,72,61,91,102,98,66,114,320,84,110,73,62,92,103,96,113,111,80,78,79,112,354,341,342,369,340,343,368,332,376,339 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#97fc934c1a9ed36f7828269de916347b751dc13ece22ed468c955e63f4b78feb, M = {66} 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 23:36:31 · history