Equation 677 Database

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Magma dd075f79545c…

magma dd075f79545c
Size
381
Isomorphism class hash
dd075f79545c13ec3afb77818581dc7a640bd23bd60c2108e2cd2a5e921af543
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 23:25:47
Display reorder
380,58,57,53,54,55,56,304,305,301,300,302,303,200,205,180,185,190,195,8,9,4,5,6,7,166,171,176,150,155,161,221,226,211,216,117,296,0,2,3,291,51,52,271,276,281,286,261,266,14,15,10,11,12,13,231,235,240,245,250,255,17,19,21,18,20,16,333,334,351,367,363,336,372,377,356,343,78,77,79,80,81,76,325,326,327,328,329,324,204,209,184,189,194,198,70,65,66,67,68,69,168,174,179,154,159,164,223,229,214,219,148,298,73,74,75,292,71,72,274,279,284,288,263,268,85,86,87,82,83,84,234,238,243,248,253,259,60,62,64,61,63,59,332,346,354,368,360,331,373,378,359,337,89,88,90,91,92,93,314,315,316,317,312,313,201,206,181,186,191,196,111,106,107,108,109,110,165,170,175,151,156,160,220,225,210,215,1,295,114,115,116,293,112,113,270,275,280,285,260,265,98,99,94,95,96,97,230,236,241,246,251,256,101,103,105,102,104,100,345,347,352,366,361,344,371,376,355,340,23,22,24,25,26,27,310,311,306,307,308,309,203,208,183,188,193,199,45,40,41,42,43,44,169,173,178,153,158,163,224,228,213,218,149,299,48,49,50,290,46,47,273,278,283,289,264,269,32,33,28,29,30,31,233,239,244,249,254,258,35,37,39,36,38,34,342,339,353,365,362,341,370,375,358,338,140,139,135,136,137,138,321,322,323,318,319,320,202,207,182,187,192,197,124,125,126,127,128,129,167,172,177,152,157,162,222,227,212,217,147,297,130,131,132,294,133,134,272,277,282,287,262,267,121,122,123,118,119,120,232,237,242,247,252,257,143,145,141,144,146,142,348,330,350,369,364,335,374,379,357,349 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 = {68} 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 23:25:48 · history