Equation 677 Database

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Magma a2e02a1dcea2…

magma a2e02a1dcea2
Size
381
Isomorphism class hash
a2e02a1dcea263f2d4f55afe430a606239f8a1a3e58970f4a3324eb958e77b17
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 23:34:53
Display reorder
380,306,308,307,311,309,310,240,245,235,259,264,254,159,149,154,144,139,116,114,289,130,121,125,194,199,204,179,184,189,80,75,275,72,64,59,49,54,44,274,39,11,16,20,29,34,215,205,210,234,224,229,164,169,174,8,9,299,99,104,109,284,89,67,294,269,94,364,369,339,349,353,374,359,344,379,334,317,316,315,313,314,312,241,246,236,256,261,251,155,146,150,141,136,115,110,286,131,120,126,191,196,201,175,180,185,81,77,277,70,61,56,45,51,40,271,35,10,15,22,25,30,216,207,212,231,220,225,161,167,171,3,1,296,95,101,106,281,85,65,290,265,90,360,366,335,345,351,371,356,341,375,331,319,318,320,321,322,323,242,247,237,255,260,250,157,147,151,140,135,117,111,285,132,122,127,190,195,200,177,182,186,82,76,276,71,60,55,46,50,41,270,36,12,17,24,26,31,217,208,213,230,221,226,162,166,170,0,2,295,96,100,105,280,86,66,291,266,91,361,365,336,346,350,370,355,340,376,330,304,303,305,301,300,302,243,248,238,257,262,252,158,148,152,142,137,118,112,287,133,123,128,192,197,202,176,181,187,83,78,278,73,62,57,47,52,42,272,37,13,18,21,27,32,218,206,211,232,222,227,163,168,172,4,5,297,97,102,107,282,87,68,292,267,92,362,367,337,347,352,372,357,342,377,332,325,324,326,327,328,329,244,249,239,258,263,253,156,145,153,143,138,119,113,288,134,124,129,193,198,203,178,183,188,84,79,279,74,63,58,48,53,43,273,38,14,19,23,28,33,219,209,214,233,223,228,160,165,173,6,7,298,98,103,108,283,88,69,293,268,93,363,368,338,348,354,373,358,343,378,333 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#890900158510c31f70f4fa8bc84bbffcea5cd35bea72b3996f708723e8ad424c, M = {73} 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 23:34:54 · history