Equation 677 Database

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Magma a17858ed220a…

magma a17858ed220a
Size
381
Isomorphism class hash
a17858ed220a0bccb17c0cbb35cf3270ac2dfefe5d7a92f1817944d26d7f1f98
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 23:21:28
Display reorder
380,43,32,20,57,24,326,9,36,50,16,30,44,18,58,25,327,14,10,37,48,15,42,31,19,59,26,328,8,38,49,41,323,34,11,0,7,45,56,52,22,324,39,35,12,23,60,5,46,54,53,325,40,21,33,13,17,6,47,55,51,2,3,29,27,28,4,370,356,357,368,330,337,331,338,373,369,287,266,288,259,242,316,253,275,297,276,264,285,289,260,240,314,277,254,272,298,278,286,265,290,258,241,315,252,274,299,279,313,268,271,282,251,292,244,257,294,311,280,269,270,295,283,249,293,245,255,312,281,296,267,273,284,250,291,243,256,246,247,263,261,262,248,346,345,360,378,359,358,334,344,343,375,124,142,157,135,164,303,175,149,131,150,143,125,158,136,162,304,151,176,147,129,152,123,141,156,137,163,305,174,148,130,122,301,144,177,155,173,126,166,133,159,300,120,145,178,160,153,171,127,167,134,302,121,161,146,179,154,172,128,165,132,168,169,139,140,138,170,336,352,354,377,366,367,353,363,355,379,105,94,82,87,113,308,70,98,112,1,92,106,80,88,114,309,119,71,99,110,76,104,93,81,86,115,310,72,100,111,103,306,96,75,77,68,107,61,117,84,329,101,97,73,85,78,69,108,62,118,307,102,83,95,74,79,67,109,63,116,66,64,91,89,90,65,332,365,371,374,341,364,342,339,340,333,208,197,212,190,216,319,230,201,183,234,195,209,210,191,217,317,235,228,202,184,236,207,196,211,189,218,318,229,203,185,206,322,199,232,239,225,181,221,188,214,320,204,200,233,215,237,226,182,219,186,321,205,213,198,231,238,227,180,220,187,223,224,194,192,193,222,351,362,372,376,349,348,350,361,347,335 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#3f9d2ac2295b056c31c59f8975f1bd5a4c115c3e4284d72341d1f63d99b23f11, 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 23:21:28 · history