Equation 677 Database

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Magma 04e147b68625…

magma 04e147b68625
Size
381
Isomorphism class hash
04e147b68625a3ae33689c9f69a3bcdfa8149af451fee4b6e2866b28446a0d42
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 23:31:47
Display reorder
380,0,37,8,58,326,51,22,44,15,30,2,38,9,59,328,31,52,23,45,16,3,39,10,54,318,32,53,18,46,17,4,40,11,55,320,33,48,19,47,12,5,41,6,56,322,34,49,20,42,13,35,36,1,7,57,324,50,21,43,14,28,24,25,26,27,29,333,335,367,331,334,332,330,350,351,368,163,141,170,156,307,155,120,148,177,134,164,142,171,157,308,135,150,121,149,178,165,143,172,158,309,136,151,122,144,179,166,138,173,159,310,137,152,123,145,174,167,139,168,160,311,132,153,124,146,175,133,140,162,169,161,306,154,125,147,176,126,128,129,130,131,127,375,374,373,365,379,344,364,345,366,346,115,93,64,108,304,107,72,100,71,86,116,94,65,109,305,87,102,73,101,66,117,95,60,110,301,88,103,74,96,67,118,90,61,111,300,89,104,75,97,68,119,91,62,112,302,84,105,76,98,69,85,92,114,63,113,303,106,77,99,70,78,80,81,82,83,79,347,358,359,378,377,348,340,360,357,339,232,204,239,225,319,218,189,211,182,203,233,205,234,226,321,198,219,190,212,183,228,206,235,227,323,199,220,191,213,184,229,207,236,222,325,200,221,186,214,185,230,208,237,223,327,201,216,187,215,180,202,209,231,238,224,329,217,188,210,181,195,197,192,193,194,196,342,376,363,361,343,341,362,371,372,349,297,271,244,289,315,287,253,279,248,269,298,272,245,290,316,264,282,254,280,246,299,273,240,291,317,265,283,255,281,250,294,274,241,292,312,266,284,256,276,249,295,275,242,293,313,267,285,257,277,251,268,270,296,243,288,314,286,252,278,247,260,262,263,258,259,261,353,352,354,355,369,338,370,356,337,336 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#7e98ac517f8529e10edd64a2dbdcf0716b1e1ea6d4bcabf776f7c383cda5136d, 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 23:31:47 · history