Equation 677 Database

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Magma f658faa14983…

magma f658faa14983
Size
381
Isomorphism class hash
f658faa149835b7ff4d1fdcb683407d5c94ee4d6da60d3ffae90cebab9d5b693
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 23:30:01
Display reorder
380,58,57,217,55,56,59,126,131,123,141,145,136,226,231,237,242,247,297,193,183,188,208,198,203,118,107,113,103,98,293,71,72,73,74,75,213,268,256,261,288,273,278,253,63,64,65,6,7,303,304,305,301,300,302,60,282,61,62,220,8,168,178,173,161,150,156,353,357,368,378,338,333,363,347,342,373,42,41,215,38,39,40,127,132,121,142,147,137,225,230,235,241,245,295,190,180,185,206,196,201,116,106,111,100,95,291,35,33,34,37,36,212,266,257,262,285,270,276,250,4,3,0,2,1,309,310,329,306,307,308,48,281,49,10,221,9,166,175,171,163,153,158,351,355,366,375,337,331,361,346,340,370,85,84,219,81,82,83,129,134,124,144,149,139,229,234,239,244,249,299,194,184,189,209,199,204,119,108,114,104,99,294,78,76,77,80,79,214,269,259,264,289,274,279,254,94,93,91,92,90,315,316,314,312,313,311,88,284,89,87,224,86,169,179,174,164,154,159,354,359,369,379,339,334,364,349,344,374,43,5,216,19,20,21,128,133,120,143,148,138,227,232,236,240,246,296,192,182,187,207,197,202,115,105,110,101,96,290,16,15,32,18,17,211,267,258,263,287,272,277,252,54,53,51,52,50,325,323,324,328,326,327,46,280,47,45,222,44,167,177,172,160,151,155,350,356,367,377,336,332,362,345,341,371,70,11,218,13,14,12,125,130,122,140,146,135,228,233,238,243,248,298,191,181,186,205,195,200,117,109,112,102,97,292,27,28,29,30,31,210,265,255,260,286,271,275,251,26,25,23,24,22,317,318,319,320,321,322,68,283,69,67,223,66,165,176,170,162,152,157,352,358,365,376,335,330,360,348,343,372 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#6034e0b6e760ca1a616002bdffba2c9ecdf9d8efbd60a04eea2e11213baf5719, M = {74} 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 23:30:02 · history