Equation 677 Database

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Magma 97f545dce64d…

magma 97f545dce64d
Size
381
Isomorphism class hash
97f545dce64dde003356140fd097f7f296819036b1de29f07c8cdaea7a300269
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 23:39:14
Display reorder
380,129,79,34,229,279,179,149,49,99,299,199,249,219,269,169,69,119,44,202,252,150,50,100,10,94,144,7,244,294,194,12,51,101,151,201,251,200,250,152,52,102,11,313,314,312,316,317,315,284,184,234,134,2,84,239,189,289,5,139,89,124,74,38,224,274,174,374,344,364,359,349,368,330,354,331,375,128,78,27,228,278,178,148,48,98,298,198,248,218,268,168,68,118,43,212,262,162,62,112,28,93,143,31,243,293,193,30,64,114,164,214,264,213,263,163,63,113,29,329,327,328,326,324,325,283,183,233,133,33,83,238,188,288,32,138,88,123,73,37,223,273,173,373,343,363,358,348,369,338,353,339,379,125,76,9,227,277,177,145,45,96,295,196,246,217,267,167,66,117,40,206,256,156,56,106,16,91,140,6,241,291,191,18,58,108,158,208,258,207,257,157,57,107,17,320,318,319,323,321,322,281,181,231,130,1,81,236,186,286,0,135,86,122,72,36,221,270,171,370,342,361,356,347,366,334,352,335,377,126,75,19,226,276,175,146,46,95,296,195,245,215,265,165,67,116,42,203,253,153,53,103,13,90,141,3,240,290,190,14,55,105,154,204,254,205,255,155,54,104,15,311,309,310,308,306,307,280,180,230,131,8,80,235,185,285,4,136,85,121,71,39,222,272,172,371,340,360,355,345,365,332,351,333,376,127,77,26,225,275,176,147,47,97,297,197,247,216,266,166,65,115,41,209,259,159,59,109,20,92,142,23,242,292,192,22,61,111,161,211,261,210,260,160,60,110,21,301,300,302,303,304,305,282,182,232,132,25,82,237,187,287,24,137,87,120,70,35,220,271,170,372,341,362,357,346,367,336,350,337,378 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#a7c342f115ba9e95260599f60b9f7eeb7d0c7792c4f4de7d123ccd3c5ebc1a9f, 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 23:39:15 · history