Equation 677 Database

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Magma 74b161dea0ff…

magma 74b161dea0ff
Size
381
Isomorphism class hash
74b161dea0ff0ee2d984f52108e6b2da099cb87b5245a12e3adc66e90e765747
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 23:26:02
Display reorder
380,158,151,162,167,172,177,148,149,144,145,146,147,277,282,287,292,297,272,142,143,138,139,140,141,130,131,126,127,128,129,133,134,135,136,137,132,309,310,311,306,307,308,192,197,202,207,182,187,212,217,222,227,232,237,262,267,242,247,252,257,6,8,10,7,9,11,356,352,334,372,362,340,354,353,367,377,157,153,163,168,173,178,0,2,3,4,5,1,278,283,288,293,298,273,45,46,47,42,43,44,54,55,56,57,58,59,64,65,60,61,62,63,321,322,323,318,319,320,193,198,203,208,183,188,213,218,223,228,233,238,263,268,243,248,253,258,48,50,52,49,51,53,359,331,345,373,363,344,338,332,368,378,156,150,161,166,171,175,90,91,92,93,94,95,276,281,285,290,295,271,80,81,82,83,78,79,67,68,69,70,71,66,72,73,74,75,76,77,304,305,301,300,302,303,191,196,200,205,181,186,211,216,221,226,230,235,260,265,241,246,251,256,87,89,85,88,84,86,358,343,346,371,361,335,330,347,366,376,155,152,160,165,170,176,119,114,115,116,117,118,275,280,286,291,296,270,106,107,102,103,104,105,101,96,97,98,99,100,122,123,124,125,120,121,329,324,325,326,327,328,190,195,201,206,180,185,210,215,220,225,231,236,261,266,240,245,250,255,113,109,111,108,110,112,357,348,333,370,360,350,349,351,365,375,159,154,164,169,174,179,39,40,41,36,37,38,279,284,289,294,299,274,25,26,27,28,29,24,15,16,17,12,13,14,20,21,22,23,18,19,313,314,315,316,317,312,194,199,204,209,184,189,214,219,224,229,234,239,264,269,244,249,254,259,31,33,35,32,34,30,355,341,336,374,364,337,339,342,369,379 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#50609e522fd5f79e53ac56beafcb5b424f2d261582798854b4ac2a2a84486b65, M = {72} 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 23:26:03 · history