Equation 677 Database

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Magma a4e5a434ac28…

magma a4e5a434ac28
Size
381
Isomorphism class hash
a4e5a434ac28b95e9ce9603c02f8e61df4130bd18ba9c02b74b9d8304c773f81
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 23:39:55
Display reorder
380,63,213,68,58,48,53,261,267,257,275,285,270,158,163,153,173,178,168,81,86,90,70,216,75,8,6,7,251,0,1,143,148,138,128,133,123,313,314,312,316,317,315,18,281,19,20,21,220,225,231,236,240,245,296,193,188,183,203,198,208,103,98,293,111,118,106,345,366,362,333,356,353,375,341,338,373,60,211,65,56,45,50,263,265,255,278,288,273,155,160,150,171,176,166,83,88,93,73,218,78,32,30,31,252,33,34,140,145,135,125,130,122,301,300,302,303,304,305,29,283,28,26,27,223,227,232,237,242,247,297,191,186,180,201,196,206,102,97,292,113,117,105,348,368,361,331,357,352,376,343,336,372,61,210,66,55,46,51,260,266,256,276,286,271,156,161,151,170,175,165,80,85,91,71,215,76,35,2,3,250,4,5,142,146,136,126,132,120,307,308,306,310,311,309,15,280,14,17,16,221,226,230,235,241,246,295,190,185,181,200,195,205,100,95,291,110,116,107,346,365,364,330,355,351,377,340,335,371,62,212,67,57,47,52,262,268,258,277,287,272,157,162,152,172,177,167,84,89,94,74,219,79,11,12,13,253,9,10,141,147,137,127,131,121,319,320,318,322,323,321,39,284,38,36,37,224,228,233,238,243,248,298,192,187,182,202,197,207,101,96,290,112,115,109,349,367,360,332,358,350,378,344,337,370,64,214,69,59,49,54,264,269,259,279,289,274,159,164,154,174,179,169,82,87,92,72,217,77,41,42,40,254,44,43,144,149,139,129,134,124,325,326,324,328,329,327,24,282,25,22,23,222,229,234,239,244,249,299,194,189,184,204,199,209,104,99,294,114,119,108,347,369,363,334,359,354,379,342,339,374 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#a7c342f115ba9e95260599f60b9f7eeb7d0c7792c4f4de7d123ccd3c5ebc1a9f, 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 23:39:55 · history