Equation 677 Database

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Magma f964dff7d152…

magma f964dff7d152
Size
381
Isomorphism class hash
f964dff7d152d8d61c995f0380cd665a3e0dfba3a0df1f9d86ac7467f522b5f9
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 23:17:32
Display reorder
380,33,32,34,35,30,31,151,156,160,165,170,175,39,40,41,36,37,38,54,55,56,57,58,59,276,281,285,290,295,271,236,210,215,221,226,231,250,256,261,266,240,245,42,43,44,45,46,47,311,306,307,308,309,310,206,180,185,191,196,201,51,50,52,53,48,49,336,355,331,371,339,366,340,376,351,356,68,67,69,70,71,66,153,158,164,169,173,178,72,73,74,75,76,77,62,63,64,65,60,61,279,284,289,293,299,274,238,213,218,224,229,233,253,259,264,269,244,248,80,81,82,83,78,79,317,312,313,314,315,316,208,183,188,194,199,203,89,88,84,85,86,87,335,358,349,370,341,367,342,375,353,360,27,26,28,29,24,25,150,155,161,166,171,176,7,8,9,10,11,6,5,1,0,2,3,4,275,280,286,291,296,270,235,211,216,220,225,230,251,255,260,265,241,246,13,14,15,16,17,12,305,301,300,302,303,304,205,181,186,190,195,200,22,21,23,18,19,20,337,357,334,372,332,365,338,377,352,362,96,101,97,98,99,100,154,159,163,168,174,179,107,102,103,104,105,106,93,94,95,90,91,92,278,283,288,294,298,273,239,214,219,223,228,234,254,258,263,268,243,249,112,113,108,109,110,111,323,318,319,320,321,322,209,184,189,193,198,204,115,114,116,117,118,119,333,359,348,373,343,368,344,378,354,363,126,131,127,128,129,130,152,157,162,167,172,177,137,132,133,134,135,136,123,124,125,120,121,122,277,282,287,292,297,272,237,212,217,222,227,232,252,257,262,267,242,247,142,143,138,139,140,141,329,324,325,326,327,328,207,182,187,192,197,202,145,144,146,147,148,149,330,361,347,374,345,369,346,379,350,364 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#09de7e296fafc11e1910887718202808c6591641f036fb4e85591d955a2aaea1, 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 23:17:33 · history