Equation 677 Database

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Magma 26c03054643c…

magma 26c03054643c
Size
381
Isomorphism class hash
26c03054643c97ef7b6f685dd61bba7f6e261054ab0c21fc5db855d829fe96c3
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 23:25:34
Display reorder
380,323,322,318,319,320,321,213,218,193,198,203,208,288,298,148,153,158,143,163,168,173,178,183,188,76,282,292,77,74,75,66,67,62,63,64,65,253,258,263,268,273,278,61,56,57,58,59,60,68,69,70,71,72,73,233,238,243,248,223,227,80,82,78,81,83,79,374,367,345,353,378,348,336,330,358,364,311,310,306,307,308,309,211,216,190,195,201,206,285,295,145,151,156,141,160,165,171,176,181,186,111,283,293,108,109,110,101,96,97,98,99,100,250,255,260,265,270,275,94,95,90,91,92,93,103,104,105,106,107,102,231,236,241,246,220,226,88,84,86,89,85,87,370,365,337,351,377,342,346,335,355,360,329,328,324,325,326,327,210,215,191,196,200,205,286,296,146,150,155,140,161,166,170,175,180,185,46,280,290,43,44,45,32,33,34,35,36,31,251,256,261,266,271,276,28,29,30,25,26,27,40,41,42,37,38,39,230,235,240,245,221,225,21,23,19,22,24,20,372,369,340,352,376,343,341,334,356,362,316,315,317,312,313,314,212,217,192,197,202,207,287,297,147,152,157,142,162,167,172,177,182,187,136,284,294,137,138,139,127,128,129,124,125,126,252,257,262,267,272,277,119,120,121,122,123,118,135,130,131,132,133,134,232,237,242,247,222,228,117,113,115,112,114,116,371,368,331,354,379,344,347,332,357,361,305,304,301,300,302,303,214,219,194,199,204,209,289,299,149,154,159,144,164,169,174,179,184,189,1,281,291,47,48,49,8,9,10,11,12,7,254,259,264,269,274,279,14,15,16,17,18,13,2,3,4,5,6,0,234,239,244,249,224,229,55,51,53,50,52,54,373,366,339,350,375,349,333,338,359,363 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 = {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 23:25:35 · history