Equation 677 Database

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Magma 9968c884fa51…

magma 9968c884fa51
Size
381
Isomorphism class hash
9968c884fa51e3124a5024b68c768b9960566dce1a7db704f74088b5166b4b3e
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 23:46:11
Display reorder
380,180,130,231,281,30,80,75,125,175,224,275,25,172,222,272,22,72,122,285,36,86,136,185,235,152,202,252,2,52,102,273,23,73,123,173,226,145,195,245,295,45,95,303,304,305,301,300,302,121,171,221,271,21,71,174,223,274,24,74,124,241,141,291,41,91,191,340,365,335,353,338,377,374,362,355,354,183,134,233,283,33,83,66,116,166,216,266,16,168,218,268,18,68,118,288,38,88,139,189,238,178,229,278,28,78,128,269,19,69,119,169,219,148,199,249,298,48,98,325,326,327,328,329,324,117,167,217,267,17,67,170,220,270,20,70,120,244,144,294,43,93,194,330,369,333,332,352,376,372,360,358,341,181,131,230,280,31,81,62,112,162,212,262,12,151,201,250,1,51,101,286,35,85,135,186,236,176,225,276,26,76,126,264,14,64,114,164,214,146,196,246,296,46,96,319,320,321,322,323,318,113,163,213,263,13,63,165,215,265,15,65,115,240,140,290,40,90,190,349,366,339,351,350,379,373,361,356,343,184,133,234,284,34,84,57,107,157,207,257,7,159,209,259,9,59,109,289,39,89,138,188,239,179,228,279,29,79,129,260,10,60,110,160,210,149,198,248,299,49,99,310,311,306,307,308,309,108,158,208,258,8,58,161,211,261,11,61,111,243,143,293,44,94,193,331,368,336,337,348,375,371,363,359,334,182,132,232,282,32,82,50,100,150,200,251,0,155,206,256,6,56,106,287,37,87,137,187,237,177,227,277,27,77,127,253,3,53,103,156,203,147,197,247,297,47,97,313,314,315,316,317,312,105,154,205,255,5,55,153,204,254,4,54,104,242,142,292,42,92,192,345,367,346,344,347,378,370,364,357,342 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#dc50bff4268d4e886a12bccb100fd4b53117610e2c07e48d4c792db14c6c3b47, M = {69} 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 23:46:12 · history