Equation 677 Database

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Magma 86917cf8f72d…

magma 86917cf8f72d
Size
381
Isomorphism class hash
86917cf8f72d80bdce3e3f6ba242bc7ab6cf8d88a8087564d56db0bbe2beab48
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 23:16:37
Display reorder
380,33,32,34,35,30,31,21,22,23,18,19,20,14,15,16,17,12,13,37,38,39,40,41,36,194,199,204,209,184,189,314,315,316,317,312,313,27,28,29,24,25,26,264,274,284,294,249,254,229,234,239,214,219,224,179,174,175,176,177,178,244,299,259,269,279,289,346,374,338,335,339,359,337,363,369,378,42,47,43,44,45,46,63,64,65,60,61,62,56,57,58,59,54,55,48,49,50,51,52,53,192,195,200,205,181,186,326,327,328,329,324,325,69,70,71,66,67,68,261,271,281,291,246,251,225,230,235,211,216,221,9,10,11,6,7,8,240,295,255,265,275,285,340,371,347,330,348,343,331,360,366,376,99,98,100,101,96,97,87,88,89,84,85,86,80,81,82,83,78,79,103,104,105,106,107,102,193,197,203,208,183,188,320,321,322,323,318,319,93,94,95,90,91,92,263,273,283,293,248,253,228,233,238,213,218,223,173,168,169,170,171,172,243,298,258,268,278,288,350,373,342,341,336,358,344,362,368,377,136,135,137,132,133,134,121,122,123,124,125,120,118,119,114,115,116,117,110,111,112,113,108,109,190,196,201,206,180,185,301,300,302,303,304,305,126,127,128,129,130,131,260,270,280,290,245,250,226,231,236,210,215,220,73,74,75,76,77,72,241,296,256,266,276,286,352,372,332,345,351,349,353,364,365,375,146,145,147,148,149,144,158,159,160,161,156,157,1,0,2,3,4,5,152,153,154,155,150,151,191,198,202,207,182,187,306,307,308,309,310,311,166,167,162,163,164,165,262,272,282,292,247,252,227,232,237,212,217,222,141,142,143,138,139,140,242,297,257,267,277,287,357,370,354,333,356,334,355,361,367,379 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 = {76} 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 23:16:38 · history