Equation 677 Database

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Magma af19810a7e1d…

magma af19810a7e1d
Size
381
Isomorphism class hash
af19810a7e1d0335c96f462bb538e27634df5f5ea86e0754d5a1a5d49970886e
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 23:49:18
Display reorder
380,210,205,215,221,226,230,181,186,175,195,201,190,240,246,235,256,261,251,166,171,161,150,155,296,310,311,309,307,308,306,71,66,275,63,51,58,5,10,1,20,266,19,147,137,141,130,125,291,30,35,26,270,46,41,80,75,281,91,95,86,285,116,121,101,107,113,351,331,358,366,336,345,340,361,370,376,212,207,217,222,227,232,182,187,177,197,202,192,243,248,238,258,263,253,165,170,160,151,156,295,312,313,314,315,316,317,72,67,277,61,52,55,8,13,3,22,267,16,145,136,140,131,126,290,33,38,27,272,47,42,82,77,282,92,97,87,286,115,120,102,108,112,352,333,356,365,337,347,342,360,372,377,214,209,219,224,229,234,184,189,179,199,204,194,244,249,239,259,264,254,169,174,164,154,159,299,304,305,303,300,302,301,74,69,279,64,54,59,9,14,4,24,269,18,146,135,144,134,129,294,34,39,29,274,49,44,84,79,284,94,99,89,289,119,124,104,109,114,354,334,359,368,339,349,344,364,374,379,211,206,216,220,225,231,180,185,176,196,200,191,241,245,236,255,260,250,168,173,163,153,158,298,324,325,326,327,328,329,73,68,278,60,53,56,6,11,0,23,268,17,149,139,143,133,128,293,31,36,28,273,48,43,83,78,283,93,98,88,288,118,123,103,105,110,353,330,357,367,338,348,343,363,371,375,213,208,218,223,228,233,183,188,178,198,203,193,242,247,237,257,262,252,167,172,162,152,157,297,321,322,323,318,319,320,70,65,276,62,50,57,7,12,2,21,265,15,148,138,142,132,127,292,32,37,25,271,45,40,81,76,280,90,96,85,287,117,122,100,106,111,350,332,355,369,335,346,341,362,373,378 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#edf00a573dad398077d9e9a7f74ac5f2ae5601c41b127cdfd29539dca9f6b98a, 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 23:49:19 · history